We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. Gen-eral Mathematics [math. Einstein predicted a contracting universe (1917) Introduction of Cosmological Constant by Einstein 1922 the Friedmann equation predicted an expanding universe 1928 Georges Lemaitre independently concluded the same Lemaitre was the first to propose a 'primeval atom' theory, later known as the Big Bang. "Finite lifespan of solutions of the semilinear wave equation in the Einstein-de Generated on Sep 08, 2019 Page 4 of 12. Forma matemática de las ecuaciones de campo de Einstein. Later, the equation was revived and is now known as Klein-Gordon equation. Vladimir Aleksandrovich Fock's father, Aleksandr A Fock, undertook research on the growing and tending of trees. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawking-type singularity theorem for solutions to the Einstein-Klein-Gordon theory, asserting that solutions with sufficient initial contraction at a compact Cauchy surface will be future timelike geodesically incomplete. We use \abstract index notation": † We write gab for the type (2,0) tensor g † gab denotes the type (0,2) tensor given by. Grenier, Y. 4 The Dirac Equation The problems with the Klein-Gordon equation led Dirac to search for an alternative relativistic wave equation in 1928, in which the time and space derivatives are ﬁrst order. Stress Energy Quantum Tensor : Linear Approximation of the Einstein's Equation and Equivalence with the Klein-Gordon's Equation. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. In Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector fields. In this paper, we investigate two types of nonlocal soliton equations with the parity-time (PT) symmetry, namely, a two dimensional nonlocal nonlinear Schrödinger (NLS) equation and a coupled nonlocal Klein-Gordon equation. References [1]W. Piaggio” Unive. From the two derived equations and we can conclude that the divergence equation in special relativity is a statement of conservation of energy and conservation of linear momentum in the matter field. The de Sitter space is an exact solution of the vacuum Einstein equations with positive cosmological constant. More precisely, we study the exact local controllability of the incompressible Euler equation with free surface. The Einstein-Klein-Gordon system has been studied for a long time. This method is designed to provide a set of flexible, easy to use computational procedures that make it possible to explore the never before studied properties of solutions to Einstein’s. These two equations together are known as the Einstein-Klein-Gordon system. gov journal article: generation of combined maxwell-einstein-klein-gordon fields from purely gravitational cases. He held the Lucasian Professor of Mathematics at the University of Cambridge and spent the last ten years of his life at Florida State University. The reliability of the model is discussed with two examples chosen specifically. In this paper, we study the forward fundamental solution of the wave and Klein-Gordon equations on asymptotically de Sitter spaces. Université Pierre et Marie Curie - Paris VI, 2014. General Mathematics [math. and push on to explore the properties of the Klein-Gordon equation. Lindblad and A. Stress-energy tensor on spacetime satisfying Klein-Gordon equation. Klein had a broad interest in various fields of physics but is perhaps best known for the Klein-Gordon equation and the Klein-Nishina equation. equations, Dirac equation, and Klein-Gordon equation. In the low-field, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schr\"odinger system. The Klein-Gordon equation for the stationary state of a charged particle in a spherically symmetric scalar field is partitioned into a continuity equation and an equation similar to the Hamilton-Jacobi equation. Vladimir Aleksandrovich Fock attended school in St Petersburg but before he finished his high school studies, World War I broke out in 1914. The caveat being that the plane wave is a solution to the Klein-Gordon equation so long that energy and momentum follows Einstein's relation. We study the evolution of the spatially homogeneous background in the fluid representation and. In the new formulation of the method, we succeed to cover wave-Klein-Gordon systems containing "strong interaction" terms at the level of the metric, and then generalize our method in order to establish a new existence theory for the Einstein equations of general relativity. 0 in the semi-classical Einstein equation and try to nd a homogeneous and isotropic, i. Souriau also rewrote Dirac’s equation in flat space-time of five dimensions as an equation in quaternion space for 2 two-component. As a corollary of our estimates on the Klein-Gordon field, one obtains in particular exponential decay in time of spherically-symmetric solutions to the linear Klein-Gordon equation on Schwarzschild-AdS. Stress Energy Quantum Tensor : Linear Approximation of the Einstein's Equation and Equivalence with the Klein-Gordon's Equation. Abstract: We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. Instead it is giv en b y the Einstein equation E 2 = ~ p + m: (21) In p osition space w e write the energy-momen tum op erator as p ! [email protected]; (E ; ~) = (i @ @ t ~ r) (22) so that the K G. In this pa. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. Fang and Q. I am a little confused about a few papers I read on the Einstein-Klein-Gordon (EKG) equations. In dimensions (three space dimensions and one time dimension), it is given by. Equivalence of Heisenberg's equation to the Schrödinger equation For the sake of pedagogy, the Heisenberg picture is introduced here from the subsequent, but more familiar, Schrödinger picture. 2008, we solve the formal solution to the equation of radiative transfer for a grid of rays through the 6"x6" simulation volume to calculate the thermal X-ray emission from the diffuse hot gas. Accordingly, the Klein-Gordon (KG) equation and Dirac equation are restudied and compared with the Relativistic Stationary Schr¨odinger Equation (RSSE). NMR and ESR (essential ideas only). "Semilinear Klein-Gordon Equation in the Friedmann-Lamaitre-Robertson-Walker spacetime," Yamagata University, Japan, Yamagata, Japan. [email protected] (Received September 16, 2014) 1. Equivalence of Heisenberg's equation to the Schrödinger equation For the sake of pedagogy, the Heisenberg picture is introduced here from the subsequent, but more familiar, Schrödinger picture. We rewrite the complex Klein-Gordon (KG) equation with a mexican-hat scalar ﬁeld potential in a thermal bath with one loop contribution as a new Gross-Pitaevskii-like equation. I am a little confused about a few papers I read on the Einstein-Klein-Gordon (EKG) equations. The expectation value of an observable A , which is a Hermitian linear operator , for a given Schrödinger state | ψ ( t )〉, is given by. Introduction The classical Einstein-Klein-Gordon eld Quantum elds Quantum strong energy inequality and the Hawking singularity theorem Eleni-Alexandra Kontou in collaboration with Christopher Fewster and Peter Brown A Celebration of Mathematical Relativity University of Miami December 16th, 2018. A complete understanding of super-radiance such as could be obtained through a time-dependent scattering theory for Klein-Gordon or Maxwell’s equations seems yet remote. These two equations together are known as the Einstein-Klein-Gordon system. If you just consider the equation [math]E^2-p^2=m^2[/math], then there's nothing forbidding [math]E[/math] from being negative. The Klein-Gordon Equation is a relativistic generalisation of the Schrordinger Equation to Relativistic Quantum Mechanics. 2 For example see Unified Field Theory based on Riemannian Metrics and distant Parallelism, Albert Einstein, Mathematische Annalen 102 (1930) pp 685-697. gov journal article: generation of combined maxwell-einstein-klein-gordon fields from purely gravitational cases. Covariant Notation for the Klein-Gordon Equation If an equation is consistent with the principles of special relativity, it should be possible to write it in covariant form, that is, in a form that is the same in all Lorentz frames. The de Sitter space is an exact solution of the vacuum Einstein equations with positive cosmological constant. us to a derivation of the Dirac equation within the scale-relativity paradigm. This single volume is a compilation of the unique lectures. This method is designed to provide a set of flexible, easy to use computational procedures that make it possible to explore the never before studied properties of solutions to Einstein's. 3 elaborates on applications to real-Scalar Fields. Quantum mechanics: Derive Schrödinger, Klein-Gordon and Dirac equations 3 of 3 A new explanation is provided that is based on doing Newtonian calculus correctly in Einstein's spacetime via. We study the Klein-Gordon and the Dirac equations in the background of the Garfinkle-Horowitz-Strominger black hole in the Einstein frame. These scalar fields therefore appear of vital importance to elucidate the possible deviations suffered by GR. We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar eld. Later, the equation was revived and is now known as Klein-Gordon equation. of the Klein-Gordon equation, E = ± p2 +m2, since the negative energy solutions have negative probability densities ρ. We now call his solution “The Dirac Equation. Indeed, the NSE may be obtained as the non-relativistic limit of the Klein–Gordon equation14, and describes the coupling of classical gravitational ﬁelds to quantum. We construct one-parameter families of solutions to the Einstein-Klein-Gordon equations bifurcating off the Kerr solution such that the underlying family of spacetimes are each an asymptotically flat, stationary, axisymmetric, black hole spacetime, and such that the corresponding scalar fields are non-zero and time-periodic. Key points for the proof of sharpness: quasimodes on Kerr-AdS 6. We consider the second quantization procedure for a KLEIN GORDON equation with time dependent Hamiltonian and with replaced second order time derivative by the appropriate difference operator. The Klein-Gordon Equation 11 We get what is known as the KleinGordon Equation, obtained in 1927 by Oskar Klein and Walter Gordon. We describe the simplest. Abstract: We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. Attractors of the Einstein-Klein Gordon System Zoe Wyatt Vacuum Einstein equations with isotropic and homogeneous T determine scale factor a(t) a_ a 2 = 8ˇG 3. The reliability of the model is discussed with two examples chosen specifically. formulations are found to lead to Klein-Gordon equation of spin-0 bosons. We analyze the the remarkable analogy between the classical Klein–Gordon equation for a test scalar field in a flat and also in a curved background, and the Gross–Pitaevskii equation for a Bose–Einstein condensate trapped by an external potential. Subsequent investigations tended to deal with the subcase of massless scalar mesons. I Maxwell equations $ electricity and magnetism I Yang-Mills equations $ strong and weak nuclear force I Dirac Equation $ quarks and leptons I Klein-Gordon Equation $ the Higgs boson I Einstein Equations $ cosmology (galaxies, dark matter, dark energy) I The impact of these equations upon mathematics, geometry in particular, cannot by. New space and time transformations in which these two equations represent a massless particle are found. The solutions may be interpreted as describing the metric g and the field {phi} in an open. Klein-Gordon equation Equation regulating the behaviour of relativistic quantum particles with spin 0. References [1]W. This paper contains one equation which accommodates both the Klein-Gordon equation for the hadron and the oscillator equation for the quarks inside the hadron. We present several classes of exact solutions in the Einstein-Klein-Gordon system with a cosmological constant. 367 (2015) 8861-8909 37. It is immediate that if the mass m vanishes, as in the case of a photon, (KGE) reduces to the standard electromagnetic wave equation (15) 1 c2 ∂2ψ ∂t2 −∇2ψ= 0,. "Finite lifespan of solutions of the semilinear wave equation in the Einstein-de Generated on Sep 08, 2019 Page 4 of 12. In Sec IV, using the algebraic method of separation of variables, we reduce the Dirac equation. The spacetime has spherical, plane, or hyperbolic symmetr. Abstract: The work shows that the evolution of the ﬁeld of the free Klein-Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density µ jyj2 subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. It is shown that the 4D Einstein-Klein-Gordon equations with a phantom scalar field (a scalar field with a negative sign in front of the kinetic energy term of its Lagrange density) has non-singular, spherically symmetry solutions. 2010 25 / 42. Introduction: Reversibility or Irreversibility & Fallibility or Infallibility. We have investigated this general approach in three special cases: First, we used the. I Maxwell equations $ electricity and magnetism I Yang-Mills equations $ strong and weak nuclear force I Dirac Equation $ quarks and leptons I Klein-Gordon Equation $ the Higgs boson I Einstein Equations $ cosmology (galaxies, dark matter, dark energy) I The impact of these equations upon mathematics, geometry in particular, cannot by. (14) comes from the consistency between the Klein-Gordon equation and the Einstein equation. How about the right side of Heisenberg's equation? Thus the action (S) shall be equal to or greater than h-bar (Planck's constant) over two. The invariance of Klein-Gordon equation under these transformations yields the Dirac equation. Both massless and massive Klein-Gordon fields in the four-dimensional Minkowski. Abstract, references and article information Full-text PDF Global regularity of solutions of the Einstein-Klein-Gordon system: A review Alexandru D. frame [28, 31, 39, 53, 54] is used. 2017 – current Research Scholar at the Institute for Advanced Physical Studies,. Equation (13) comes from the consistency of the initial value constraint and evolution equation and Eq. In the new formulation of the method, we succeed to cover wave-Klein-Gordon systems containing "strong interaction" terms at the level of the metric, and then generalize our method in order to establish a new existence theory for the Einstein equations of general relativity. Subsequent investigations tended to deal with the subcase of massless scalar mesons. In applying the obtained result to the weak gravitational. Klein-Gordon equation Equation regulating the behaviour of relativistic quantum particles with spin 0. nonlinear Klein-Gordon equation on the unbounded domain. Aleksandr Fock was later employed as an inspector of forests in the south of Russia. For Free Particles It Is A. THE STATIC EQUATIONS We give below the static equations of the Einstein-. Dirac wanted to fix the problems with the Klein-Gordon equation by seeking a new solution to it. We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. It was formulated in late 1925, and published in 1926, by the Austrian physicist Erwin Schrödinger. describing a massless or mas-sive spin-0 particle; Dirac equation for a massive spin-1/2 particle; Maxwell eqs. In classical, pre-Einstein physics, the amount of energy is given by a half times an object's mass times the square of its speed. The bounds also depend on γ and f together with its derivatives and are valid for all values of the coupling. Over the past decade, the mathematical research on Einstein equation has made spectacular progress on many fronts, including the Cauchy problem, cosmic censorship, and asymptotic behavior. Oliver Waldron and Robert A Van Gorder 2017 Phys. The Hydrodynamic Representation of the Klein-Gordon Equation with Self-Interacting Field Piero Chiarelli *. We stress here that the solution associated. The symmetric part, ~ , is the Lie derivative of the metric, which links the Klein-Gordon equation to modi ed general relativity for spins 1,1/2 and 0. Klein-Gordon equation) in the gravitational field of a stationary rotating black hole (Kerr black hole). The analogous equation for systems with half-integer spin is the Dirac Equation. In the low-field, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schrödinger system. Klein-Gordon equation. Beyera Center for Computation and Technology (CCT), Louisiana State University (LSU), 328 Johnston Hall, Louisiana 70803, USA and Max Planck Institute for Gravitational Physics, Albert Einstein Institute (AEI), Am Mühlenberg 1, D-14476 Potsdam, Germany. An exact (nonstatic) stationary solution is found such that the electric field vanishes, the magnetic field is constant and parallel to the polar axis, and the wavefunction. Labels: Dirac equation, Einstein's field equations, Klein-Gordon equation, mathematics, physics, quantum field theory, quantum physics, relativity, unified field theory No comments: Post a Comment. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawking-type singularity theorem for solutions to the Einstein-Klein-Gordon theory, asserting that. So you have two choices: (1) accept that a klein gordon field around a fixed minkowski background is not conformally invariant at the classical level, or (2) look at a different physical theory, the KG field coupled to gravity, which will exhibit the conformal symmetry. These two equations together are known as the Einstein-Klein-Gordon system. It is a quantized version of the relativistic energy-momentum relation. Voor lage energie leidde Schrödinger uit de klein-gordonvergelijking de vergelijking af die nu zijn naam draagt. Variational Principle Approach to General Relativity Chakkrit Kaeonikhom Submitted in partial fulﬂlment of the requirements for the award of the degree of Bachelor of Science in Physics B. Quantum Theory 2015/16 4. You can ﬁnd plane-wave solutions to the Klein–Gordon equation easily. We all know that the Schrödinger equation is a non relativistic wave equation. Physical cosmology is the study of the properties and evolution of the large scale structure of the universe. Reader for the course Quantum Field Theory W. Wave equations express the properties of motion in waves. "Semilinear Klein-Gordon Equation in the Friedmann-Lamaitre-Robertson-Walker spacetime," Yamagata University, Japan, Yamagata, Japan. Our motivation for initiating a study of this system is the following. 10378 Joint with David Fajman. So you have two choices: (1) accept that a klein gordon field around a fixed minkowski background is not conformally invariant at the classical level, or (2) look at a different physical theory, the KG field coupled to gravity, which will exhibit the conformal symmetry. We derive lower bounds on such averages that depend only the values of φ, but not its derivatives. We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. These two equations together are known as the Einstein-Klein. Abstract A study of the spherically symmetric eigenstates of the Klein-Gordon Einstein equations (Klein-Gordon geons) reveals that these geons have properties that are uniquely different from other gravitating systems that have been studied. Proca equation is a relativistic wave equation for a massive spin-1 particle. only time-dependent, solution of the Klein-Gordon equation fsuch the semi-classical Einstein equation holds. can be corrected to ensure that the Klein-Gordon equation holds. These two equations together are known as the Einstein-Klein-Gordon system. It is a quantized version of the relativistic energy-momentum relation. There exists a class of potentials for which the Hamilton-Jacobi equation is exactly obtained and examples of these potentials are given. Accordingly, the Klein-Gordon (KG) equation and Dirac equation are restudied and compared with the Relativistic Stationary Schr¨odinger Equation (RSSE). 2 discusses the Klein-Gordon case in the pres-ence of a cosmological constant and Sect. The geometry of Schwarzschild-AdS and Kerr-AdS 3. The de Broglie and Planck-Einstein relation are actually components of the same relativistic formula. Klein-Gordon case (main application), Subs. incorporate Special Relativity. The massless Klein-Gordon equation reduces to {r2 exp [ z ( v- ) ] tp'}'=0 (5) and is contained in the contracted Bianchi identity. ÉQUATION DE KLEIN-GORDON GÉNÉRALISÉE. In recent years, the interest in it has been renewed mainly because many alternatives to General Relativity (GR) contain scalar fields (see ref. In Chapter3, we explore spherically symmetric solutions to the Einstein-Klein-Gordon equations, the de ning equations of wave dark matter, where the scalar eld is of the form fp t;rq ei!tFp rq for some constant !P R and complex-valued function Fp rq. IVB dis-cusses the Klein-Gordon case in the presence of a cosmo-logical constant, and Subs. This equation has a form of Klein-Gordon equation in curved space [10] accounting the field of brane fluctuations and describes particle temporal behavior with Einstein's or time dependent Wheeler de - Witt equation [11]. In recent years, the interest in it has been renewed mainly because many alternatives to General Relativity (GR) contain scalar fields (see ref. Voor lage energie leidde Schrödinger uit de klein-gordonvergelijking de vergelijking af die nu zijn naam draagt. References [1]W. Covariant Notation for the Klein-Gordon Equation If an equation is consistent with the principles of special relativity, it should be possible to write it in covariant form, that is, in a form that is the same in all Lorentz frames. We consider waves, which obey the semilinear Klein-Gordon equation, propagating in the Friedmann-Lemaître-Robertson-Walker spacetimes. Este campo descreve partículas sem spin. 2017 – current Research Scholar at the Institute for Advanced Physical Studies,. The information in question is, perhaps surprisingly, not Shannon or Boltzmann entropy but, rather, Fisher information, a simple concept little known to physicists. The nonrelativistic-semiclassical limit, ~ !0;c= ~ !1for some >0, of the modulated defocusing cubic nonlinear Klein-Gordon equation is the classical wave map for the limit wave function and typical linear wave equa-tion for the associated phase function. Quantum mechanics: Derive Schrödinger, Klein-Gordon and Dirac equations 3 of 3 on doing Newtonian calculus correctly in Einstein's spacetime via quaternions. Solution for a non-homogeneous Klein-Gordon equation 685 terms of logarithmic functions, which generate singularities near the region where the solutions are not de ned. 3 Schr odinger form of the Klein Gordon Equation In addition to expressing the Klein-Gordon equation in terms of a partial di erential equation that is rst order in space and time (which by default introduces Spinors) it is also possible to express the Klein-Gordon equation as a set of coupled Schr odinger type equations thus (using natural. 1 Quick Review of Special Relativity Four-Vector Notation: The coordinates of an object or ‘event’ in four-dimensional space-. (12) We should observe here that the ﬁeld equation and the Lagrangian reduce to those of minimal coupling for ﬂat spacetimes but the stress-energy tensor does not. AN INTRINSIC HYPERBOLOID APPROACH FOR EINSTEIN KLEIN-GORDON EQUATIONS QIAN WANG Abstract. The Einstein’s field equations with the cosmological term are given by (2) where (3) (4) and (5) are respectively the energy momentum tensors for the perfect fluid and massless scalar field. Previously reported work developed the CCM framework for the coupled Einstein-Klein-Gordon system of equations, assuming a regular center of symmetry. Il a alors obtenu l'équation connue aujourd'hui sous le nom de Klein-Gordon, mais son application au cas du potentiel coulombien donnant des niveaux d'énergie incompatibles avec les résultats expérimentaux de l'atome d'hydrogène [4], il se serait rabattu sur le cas non-relativiste, avec le succès que l'on connait. 0 in the semi-classical Einstein equation and try to nd a homogeneous and isotropic, i. Abstract We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. From here we can determine the energy of the ground state (f=frequency): We get an interesting result. wcuum Einstein or Einstein-Klein-Gordon equations. These two equations together are known as the Einstein-Klein-Gordon system. 1 Einstein ﬂeld equations: overview Let us consider a ﬂxed \space time" (M;g). and push on to explore the properties of the Klein-Gordon equation. Université Pierre et Marie Curie - Paris VI, 2014. Einstein Online is provided by the Klein-Gordon equation Equation regulating the behaviour of relativistic quantum particles with spin 0. A singularity theorem for Einstein–Klein–Gordon theory Page 5 of 24 121 where the conformal coupling constant ξc is deﬁned as ξc = n −2 4(n −1) (12) We should observe here that the ﬁeld equation and the Lagrangian reduce to those. 92 105001 We begin our discussion with a review of the progress made by Xiong et al [15], by describing the phenomenology of a superfluid in curved spacetime in terms of a complex scalar field Φ satisfying a nonlinear Klein-Gordon equation. In this paper, we solve the static, massive Einstein-Klein-Gordon (EKG) equations in perturbation, and compare the results with a similar. We describe the simplest solutions of these systems in spherical symmetry, the spherically symmetric static states, and some scaling properties they obey. In [7] Klainerman introduced the hyperboloidal method to prove the global existence results for nonlinear Klein-Gordon equations by using commuting vector ﬁelds. So er, Scattering for the Klein-Gordon Equation with quadratic and variable coe cient Cubic nonlinearities. Klein{Gordon equation in AdS5 Yp;qand derive an integral representation thereof for both the homogeneous and inhomogeneous Cauchy problem (Theorem 10 and Corollary 11). Isotropic cosmologies are discussed, and it is shown how the approach of Ellis et al. Volume 7, Issue 2 Ver. where H is the Hamiltonian and [·,·] is the commutator of A and H. By considering a random walk model compounded in Einstein's evolution equation, we show that both the classical Schro¨dinger and Klein-Gordon equations can be viewed as a consequence of introduc-ing a memory function given by −iδ and δ(1), respectively. Epilogue: A non-linear model: Asymptotic stability of Scwharzschild-AdS for the spherically symmetric Einstein-Klein-Gordon system. As for the massless case the solutions have a naked singularity at the origin. The Klein Gordon equation is an attempt to marry special relativity and quantum mechanics. In this paper we calculate the Bondi mass of asymptotically flat spacetimes with interacting electromagnetic and scalar fields. Solution for a non-homogeneous Klein-Gordon equation 685 terms of logarithmic functions, which generate singularities near the region where the solutions are not de ned. It is derived from Einstein's energy equation where the energy and momentum terms are replaced with quantum mechanical operators. PHYSICS FROM FISHER INFORMATION A Uniﬁcation This book deﬁnes and develops a unifying principle of physics, that of ‘extreme physical information’. In the low- eld, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schr odinger system. 2), and the same is true for the solutions of the free Dirac. In this pa. We derive lower bounds on such averages that depend only the values of φ, but not its derivatives. NNT: 2014PA066379. We rewrite the complex Klein-Gordon (KG) equation with a mexican-hat scalar ﬁeld potential in a thermal bath with one loop contribution as a new Gross-Pitaevskii-like equation. In recent years, the interest in it has been renewed mainly because many alternatives to General Relativity (GR) contain scalar fields (see ref. In particle physics, the Dirac equation is a relativistic wave equation derived by British physicist Paul Dirac in 1928. The stress-energy tensor involves the use of superscripted variables (not exponents; see tensor index notation and Einstein summation notation). asymmetric wave equation can then be symmetrized. 2008, we solve the formal solution to the equation of radiative transfer for a grid of rays through the 6"x6" simulation volume to calculate the thermal X-ray emission from the diffuse hot gas. Partial differential equations and applied analysis Nonlinear Schr odinger equation and applications in Bose-Einstein the Klein-Gordon equation in the. Klein -Gordon equation. Both contributions to the noise kernel are separately conserved, since both and satisfy the Klein-Gordon field equations on the background spacetime. gov journal article: a class of eigenvalues of the fine-structure constant and internal energy obtained from a class of exact solutions of the combined klein--gordon--maxwell--einstein field equations. effect on the behaviour of solutions to the Klein-Gordon equation on this background. I Maxwell equations $ electricity and magnetism I Yang-Mills equations $ strong and weak nuclear force I Dirac Equation $ quarks and leptons I Klein-Gordon Equation $ the Higgs boson I Einstein Equations $ cosmology (galaxies, dark matter, dark energy) I The impact of these equations upon mathematics, geometry in particular, cannot by. Wave equations express the properties of motion in waves. How to use the einstein energy-momentum relation to derive the Klein Gordon Wave Equation. iosrjournals. An intrinsic hyperboloid approach for Einstein Klein-Gordon equations, arXiv:1607. He then derives the action, Lagrangian, and equations of motion for this case, and shows that the equations of motion are wave equations with a singularity at the location of the particle. In the low- eld, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schr odinger system. 3 elaborates on applications to real-Scalar Fields. Using methods developed by Fewster and Galloway, these lower bounds are applied to prove a Hawking-type singularity theorem for solutions to the Einstein-Klein-Gordon theory, asserting that solutions with sufficient initial contraction at a compact Cauchy surface will be future timelike geodesically incomplete. We describe the simplest. In applying the obtained result to the weak gravitational. where , is the gravitational constant in Einstein’s equations, and the “mass”-term of the 5-dimensional wave equation, i. This explains where this tensor gets its name: energy-momentum tensor. Annals of Math. In the new formulation of the method, we succeed to cover wave-Klein-Gordon systems containing "strong interaction" terms at the level of the metric, and then generalize our method in order to establish a new existence theory for the Einstein equations of general relativity. We describe the simplest. equation is called Klein–Gordon equation. describing a massless or mas-sive spin-0 particle; Dirac equation for a massive spin-1/2 particle; Maxwell eqs. Ray Diffraction, Schottky defects. Download with Google Download with Facebook or download. In 1947, utiyama13 examined the Einstein equations with a scalar meson source which obeyed a curved spacetime version of the Klein-Gordon equation. De Sitter space is a solution of the Einstein equations of general relativity with positive cosmological. In some sense, the Heisenberg picture is more natural and fundamental than the Schrödinger picture, especially for relativistic theories. ear Klein-Gordon equation is the defocusing nonlinear Schr odinger equation. ential equations, the relativistic Vlasov-Klein-Gordon system, we prove local- in-time existence of classical solutions and a continuation criterion which says that a solution can blow up only if the particle momenta become large. gravitational potential. Abstract, references and article information Full-text PDF Global regularity of solutions of the Einstein-Klein-Gordon system: A review Alexandru D. So if you have a tensor equation, then you get diffeomorphism covariance for free. Dirac Equation. It is the equation of motion of a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Este campo descreve partículas sem spin. In this pa. In classical, pre-Einstein physics, the amount of energy is given by a half times an object's mass times the square of its speed. Exact Solutions > Linear Partial Differential Equations > Second-Order Hyperbolic Partial Differential Equations > Linear Klein-Gordon Equation 2. Abstract: The work shows that the evolution of the ﬁeld of the free Klein-Gordon equation (KGE), in the hydrodynamic representation, can be represented by the motion of a mass density µ jyj2 subject to the Bohm-type quantum potential, whose equation can be derived by a minimum action principle. New space and time transformations in which these two equations represent a massless particle are found. It is second-order in space and time and manifestly Lorentz-covariant. Of course if m = 0 there is no distinction between the two factors. and push on to explore the properties of the Klein-Gordon equation. These two equations together are known as the. Still Wyman starts by integrating the Klein-Gordon equation: 2. De Sitter space is a solution of the Einstein equations of general relativity with positive cosmological. When the relation is applied to a four-vector field A μ {\displaystyle A^{\mu }} instead of a Lorentz scalar field ψ {\displaystyle \psi } , then one gets the Proca equation (in Lorenz gauge ):. It is immediate that if the mass m vanishes, as in the case of a photon, (KGE) reduces to the standard electromagnetic wave equation (15) 1 c2 ∂2ψ ∂t2 −∇2ψ= 0,. For a memory function of the type −i1+αδ(α) where 0 <α<1 we derive. A Lagrange multiplier λ is used as a constraint to properly couple matter with gravity. Dirac, however, knew that the Schrödinger Equation needed to be made Lorentz invariant if it was to be correct, and believed that modifying the Klein-Gordon Equation was the best way to go about that. The Klein-Gordon Equation or the Klein-Fock-Gordon Equation is an equation in quantum field theory which initially was discovered by Schrodinger but discarded by him soon after. The Klein-Gordon Equation in the Anti-de Sitter Spacetime, Rendiconti del Seminario Matematico dell’ Universita’ e del Politecnico di Torino, 67(2009), pp. Modi ed general relativity is intrinsically hidden in the Klein-Gordon equation for spins 2 and 3/2. com Abstract : Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon's equation. The proof relies on estimates developed for the linear wave equation by the second author and. Gen-eral Mathematics [math. Instead it is giv en b y the Einstein equation E 2 = ~ p + m: (21) In p osition space w e write the energy-momen tum op erator as p ! [email protected]; (E ; ~) = (i @ @ t ~ r) (22) so that the K G. Ray Diffraction, Schottky defects. Both integrated decay and pointwise decay estimates are obtained. As for the massless case the solutions have a naked singularity at the origin. Reader for the course Quantum Field Theory W. The part one presents what the Klein-Gordon’s equation and the integration of the theory of quantum information in it. Download with Google Download with Facebook or download. The Klein-Gordon field on a signature-changing background is discussed, and it is shown how the approach of Dray et al. In addition to the requirement of the Einstein Field equation, once the scalar ﬁeld was added to the system, it needed to satisfy its own diﬀerential equation, the Klein-Gordon equation. Recall that this corresponds to the other factor of the equation E 2 – p 2 – m 2 = 0, so solutions of this equation are, strictly speaking, equally valid solutions of the Klein-Gordon equation from which we began. Il a alors obtenu l'équation connue aujourd'hui sous le nom de Klein-Gordon, mais son application au cas du potentiel coulombien donnant des niveaux d'énergie incompatibles avec les résultats expérimentaux de l'atome d'hydrogène [4], il se serait rabattu sur le cas non-relativiste, avec le succès que l'on connait. can be corrected to ensure that the Klein-Gordon equation holds. This is a joint work with Pietro Baldi and Daniel Han-Kwan. IVB dis-cusses the Klein-Gordon case in the presence of a cosmo-logical constant, and Subs. New space and time transformations in which these two equations represent a massless particle are found. Nonlinear Klein-Gordon equation and its application on f(R) theory of gravitation. About Einstein Online. The study of relativistic particles in static magnetic fields has a long history and is still attracting considerable attention, especially for cases where someone deals with curv. com Abstract : Our goal in this paper is to study the relationship between the linear approximation of Einstein's equations to the Klein-Gordon's equation. Emmanuel Hebey. Abstract: In this paper the quantum hydrodynamic approach for the Klein-Gordon equation (KGE) owning a perturbative self-interaction term is developed. We study the evolution of the spatially homogeneous background in the fluid representation and. Letters in Mathematical Physics, 2000. The Oskar Klein Memorial Lecture series has become a very successful tradition in Swedish physics since it started in 1988. It is believed that every relativistic quantum model describing a system without external interactions (a free system) is, in a sense, a special case of the Klein-Gordon equation; in particular, every solution of the potential formulation of free Maxwell's equations satisfies (3. In 1925, De Broglie published the symmetric relation between momentum andwavelength, λ = h/p, now called the De Broglie relation. The quantum potential, derived from the Klein-Gordon equation, allows for matter's intrinsic interaction with spacetime. These two equations together are known as the Einstein-Klein-Gordon system. The sharp log decay result 4. Klein -Gordon equation. Abstract We examine the Einstein equation coupled to the Klein-Gordon equation for a complex-valued scalar field. Nonlinear Klein-Gordon equation and its application on f(R) theory of gravitation Yue Ma To cite this version: Yue Ma. NNT: 2014PA066379. But why did it need to be of first order in time- and spatial-derivatives? Is. governed by a D’Alembertian equation in higher dimensional space-time, which results to be equivalent either to a Klein-Gordon equation (to describe bosons) or a Dirac equation (to describe fermions) in four Science Publishing Group 71. This equation was actually discovered by Erwin Schrodinger before he. can be corrected to ensure that the Klein-Gordon equation holds. The Heisenberg picture is another formulation of QM, in which case the wavefunction ψ is time-independent, and the operators A(t) contain the time dependence, governed by the equation of motion:. We interpret. When an electron is bound in a Hydrogenlikeatom with pointlikenucleus havingcharge number Z, thecritical value of Z, Zc, equals to 137 in Dirac equation whereas. IVC and IVD discuss, as we mentioned earlier, applications to real scalar ﬁelds and to Klein-Gordon geons respectively. fr | RomanBaudrimont. In the low-field, non-relativistic limit, the Einstein-Klein-Gordon system reduces to the Poisson-Schr\"odinger system. The scalar and vector potentials in Maxwell theory are shown to be of physical signiﬂcance in Proca formulation. We describe the simplest. Abstract： The s-wave Klein--Gordon equation for the bound states is separated in two parts to see clearly the relativistic contributions to the solution in the non-relativistic limit. The Klein Gordon equation is an attempt to marry special relativity and quantum mechanics. En las ecuaciones de campo de Einstein, la gravedad se da en términos de un tensor métrico, una cantidad que describe las propiedades geométricas del espacio-tiempo tetradimensional y a partir de la cual se puede calcular la curvatura. Where does the factor of half appear from in the. The quantum axion field satisfies the Klein-Gordon equation in a curved space-time and the metric components of this space-time are solutions to the Einstein equations with a source term given by the vacuum expectation value of the energy-momentum operator constructed from the axion field. These two equations together are known as the Einstein-Klein-Gordon system. The idea of Dirac was to demand that there be Hamiltonian that is linear in such the square of would give the required formula. Dirac cherchait à transformer l'équation de Schrödinger afin de la rendre invariante par l'action du groupe de Lorentz, en d'autre termes à la rendre compatible avec les principes de la relativité restreinte. The plane waves (10) are basic solutions and the field (9) is constructed by. We now call his solution “The Dirac Equation. The massless Klein-Gordon equation reduces to {r2 exp [ z ( v- ) ] tp'}'=0 (5) and is contained in the contracted Bianchi identity. the test Klein-Gordon and Hamilton-Jacobi equations allow for the separation of variables. Dirac, however, knew that the Schrödinger Equation needed to be made Lorentz invariant if it was to be correct, and believed that modifying the Klein-Gordon Equation was the best way to go about that. Klein -Gordon equation. 2017 – current Research Scholar at the Institute for Advanced Physical Studies,. Beyera Center for Computation and Technology (CCT), Louisiana State University (LSU), 328 Johnston Hall, Louisiana 70803, USA and Max Planck Institute for Gravitational Physics, Albert Einstein Institute (AEI), Am Mühlenberg 1, D-14476 Potsdam, Germany.