Comparison among kleingordon equation, dirac equation and. An exact stationary solution of the combined einsteinmaxwell. Pdf we extend the analogue spacetime program by investigating a condensedmatter system that is in principle capable of simulating the massive. We examine the einstein equation coupled to the kleingordon equation for a complexvalued scalar field. Modi ed general relativity and the kleingordon equation in. Pdf relativistic point dynamics and einstein formula as. Iii we separate variables and solve the klein gordon equation. A singularity theorem for einsteinkleingordon theory page 5 of 24 121 where the conformal coupling constant. We examine the einstein equation coupled to the kleingordon equation for a complexvalued scalar. These two equations together are known as the einstein klein gordon system. As we have seen, this is a sensible notion only in the limit where the ball is very small. Subject to the other conditions of theorem 3, the bound 67 is valid.
The klein gordon equation klein fock gordon equation or sometimes klein gordon fock equation is a relativistic wave equation, related to the schrodinger equation. The stationary einsteinmaxwell kl eingordon emkg equations for interacting gravitational, electromagnetic, and meson fields are examined. Variational principle approach to general relativity chakkrit kaeonikhom submitted in partial ful. Klein gordon equation f eynman stuec k elburg in terpretation dirac equation an tiparticles f ermion spin co v arian t notation massless fermions learning outcomes be able to deriv e k g equation and explain ph ysical meaning of v e e solutions. In the low eld, nonrelativistic limit, the einsteinkleingordon system reduces to the poissonschr odinger system. As we can see now, the apparent problems were manifestations of the new physics. Variational principle approach to general relativity. Therefore, as long as energy and momentum follows the einsteins relation eq. Jun 04, 2018 how to use the einstein energymomentum relation to derive the klein gordon wave equation. China weimin zhouy and jun yanz department of physics, new york university, 4 washington place, new york, ny, 3 a particle is always not pure. Difficulties with the klein gordon equation unfortunately, the density associated with the time component of the current, ih h i 1 0. We describe the simplest solutions of these systems in spherical symmetry, the spherically.
The gravity of the classical kleingordon field mdpi. The dynamics of the model is governed by the coupled. Attractors of the einsteinklein gordon system zoe wyatt. Each component of the wave function of particles of any spin also satisfies the kleingordon equation, but only for the case where the spin is 0 is the function invariant with respect to the lorentzpoincare group.
In the same year of 1926, klein 2, gordon 3 and fock 4 developed the relativistic quantum mechanical wave equation. Part 1 presents what the klein gordon equation and the integration of the. From einstein to kleingordon quantum mechanics and relativity aline ribeiro department of mathematics university of toronto march 24, 2002 abstract we study the development from einsteins relativistic energymomentum relation for free particles, e2. Using methods developed by fewster and galloway, these lower bounds are applied to prove a hawkingtype singularity theorem for solutions to. It is secondorder in space and time and manifestly lorentzcovariant. Stability of schwarzschildads for the spherically symmetric. Dec 25, 2012 in this paper, we study the global behavior of solutions to the spherically symmetric coupled einsteinkleingordon ekg system in the presence of a negative cosmological constant.
How to use the einstein energymomentum relation to derive the klein gordon wave equation. In particle physics, the dirac equation is a relativistic wave equation derived by british physicist paul dirac in 1928. The kleingordon equation kleinfockgordon equation or sometimes kleingordonfock equation is a relativistic wave equation, related to the schrodinger equation. 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. Both the kleingordon and the dirac equation are no 1particle waveequations, but relativistic. The theory is cast into the formalism of principal fiber bundles with a connection, wherein its relationship to current trends in theoretical physics is made manifest. Mar 29, 2018 using methods developed by fewster and galloway, these lower bounds are applied to prove a hawkingtype singularity theorem for solutions to the einstein klein gordon theory, asserting that. Our goal in this paper is to study the relationship between the linear approximation of einsteins equations to the kleingordons equation.
Hydrodynamic representation of the kleingordoneinstein. I go over fourvector notation, fourgradient, and writing the equation in terms of the dalambertian. Its theoretical relevance is similar to that of the dirac equation. 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 of the matter field is of the form of a pure. These two equations together are known as the einsteinkleingordon system. He then tried to find solutions, but was dismayed to find that problems like nonpositivedefinite probability curre. Over a decade before that, einstein 5 formulated general relativity gr in 1915. The einsteinkleingordon equations, wave dark matter, and the. Suppose \m,g,\phi \ is a solution to the einsteinkleingordon equation with any additional matter obeying both the strong and weak energy conditions. The interaction of pseudo scalar particles with the electromagnetic field is described by the minimal substitution. From einstein to kleingordon quantum mechanics and relativity. In the lowfield, nonrelativistic limit, the einsteinkleingordon system reduces to the poissonschrodinger system. B the einsteinkleingordon equations in spherical symmetry. We examine the einstein equation coupled to the klein gordon equation for a complexvalued scalar field.
It is a quantized version of the relativistic energymomentum relation. Deriving the klein gordon equation relativistic quantum. The plane waves 10 are basic solutions and the field 9 is constructed by. In the lowfield, nonrelativistic limit, the einstein klein gordon system reduces to the poissonschr\odinger system. Subsequent investigations tended to deal with the subcase of massless scalar mesons. Approximation linear of the einstein equations and equivalence with the kleingordon equation roman.
In sec iv, using the algebraic method of separation of variables, we reduce the dirac equation. A singularity theorem for einsteinkleingordon theory. In the low eld, nonrelativistic limit, the einstein klein gordon system reduces to the poissonschr odinger system. Kleingordon equation relativistic quantum mechanics. I am a little confused about a few papers i read on the einsteinkleingordon ekg equations. Comparison among kleingordon equation, dirac equation and relativistic stationary schr. We examine the einstein equation coupled to the klein gordon equation for a complexvalued scalar eld. What is the relationship between the dirac equation and the. The einsteinmaxwellkleingordon equations are simplified by imposing stationarity, isometric motion, the weylmajumdarpapapetrou condition, and axial symmetry. J, c mc2 t t 29 is not positive definite, as we require of a probability density. So, none of the objections that led to discarding the klein equation held up with time. We examine the einstein equation coupled to the kleingordon equation for a complexvalued scalar eld.
First, we will reduce the kleingordon equation to rst order form by introducing the auxiliary variables. Separation of variables and exact solution of the klein. Einsteinkleingordon equations in spherical symmetry. Relativistic point dynamics and einstein formula as a property of localized solutions of a nonlinear klein gordon equation article pdf available in communications in mathematical physics 3222. The part one presents what the kleingordons equation and the integration of the theory of quantum.
That is, the klein gordon equation seems to lead to negative. Pdf einsteinkleingordon system by gravitational decoupling. In 1947, utiyama examined the einstein equations with a scalar meson source which obeyed a curved spacetime version of the klein gordon equation. Pdf massive kleingordon equation from a boseeinstein. Aug 23, 2019 that method takes advantage of the commutation properties of the maxwell and klein. Since the detailed stochastic hydrodynamic derivation of 62 shows that the. The einsteinkleingordon equations, wave dark matter, and. 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 nonsingular, spherically symmetry solutions. From what i understood one takes the energystresstensor of the scalar field. Cauchycharacteristic evolution of einsteinkleingordon systems. Linear approximation of the einsteins equations and equivalence with the kleingordons equation. It has also been proposed that dark matter dm halos may be made of a sf described by the kge equations see, e.
In its free form, or including electromagnetic interactions, it describes all spin1 2 massive particles such as electrons and quarks for which parity is a symmetry. The kleingordon equation in the spacetime representation 9 the quantity q2 is represented by the differential operator dalembert operator from the mass shell condition 6 this results in the kleingordon equation as the basic field equation of the scalar field. The hydrodynamic representation of the kleingordon equation kge. Jul 08, 2015 we examine the einstein equation coupled to the kleingordon equation for a complexvalued scalar field. Kleingordon equation relativistic quantum mechanics youtube. Its solutions include a quantum scalar or pseudoscalar field, a field whose quanta are spinless particles. Lecture notes on general relativity matthiasblau albert einstein center for fundamental physics institut fu. Pdf a singularity theorem for einsteinkleingordon theory. Hydrodynamic representation of the kleingordon einstein.
Gordon equations with the generators of the poincare group to resolve the difficulties caused by the fact that they have, separately, different asymptotic properties. Relativistic quantum mechanics kleingordon equation dirac. In that year, he published three articles, on light quanta, on brownian motion, and on the foundations of the theory of special relativity and, almost as an afterthought, a short note containing a. Later, the equation was revived and is now known as kleingordon equation. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. If we start with such a ball of particles, it will, to second order in time.
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