It is a quantized version of the relativistic energymomentum relation. The initial part of the derivation of the standard dirac equation, is a reformulation of the klein gordon, which is then augmented via the insertion of diracs gamma matrices, to account for both clockwise and anticlockwise spin, and for both positive and negative energy solutions. The kleingordon equation is a relativistic wave equation, related to the schrodinger equation. Covariant notation for the kleingordon 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.
If you like you can view the kleingordon equation as a \toy model for the maxwell equations. If you like you can view the klein gordon equation as a \toy model for the maxwell equations. We follow a roughly historical order in pre senting this material. Pdf logical inference approach to relativistic quantum.
Didactic derivation of the special theory of relativity. How to use the einstein energymomentum relation to derive the klein gordon wave equation. Since the terms required for invariance correspond with known quantum effects, no. Kleingordon equation derivation and continuity equations 3 energies, were taken to be major problems with the kleingordon equation which led to it being disregarded initially as a valid relativistic equation. Jun 04, 2018 how to use the einstein energymomentum relation to derive the klein gordon wave equation. The non relativistic limit of the real kleingordon equation.
The derivation can then allow the use of potentials as constraints along with the. The schrodinger and kleingordon equations are directly derived from classical. Derivation of solutions of the kleingordon equation from solutions of the wave equation volume 15 issue 2 ll. It is shown that the kleingordon equation for a massive, charged, and spinless particle derives from the combination of the requirements that the spacetime data collected by probing the particle is obtained from the most robust experiment and that on average.
Kleingordon quantum equation was also derived from the same maxwells equation by utilizing resemblance between electric field vector and wave function in. The quantum mechanical origin of the kleingordon equation hides its capability to model many classical systems. So the kleingordon eld is physically and mathematically, too the simplest of the relativistic elds that one can study. Relativistic quantum mechanics kleingordon equation dirac. In particular, it was already shown that the eulerlagrange equation is the kleingordon equation exercise 2. That is where cryptohermitian approach can be applied. For some calculations it is useful to write the kleingordon equation in the twocomponent form 4. Derivation of klein gordon equation from maxwells electric. Derivation of the schrodinger equation and the kleingordon equation from first principles gerhard grossing austrian institute for nonlinear studies parkgasse 9, a1030 vienna, austria abstract. Pdf notes on the kleingordon equation researchgate. The state of a system is described by a state vector. Derivation of klein gordon equation or relativistic schrodinger equation, klein gordan equation is relativistic wave equation. Akgun department of electronics engineering gebze institute of technology gebze, kocaeli, turkey abstractan initialboundary value problem for the system of.
The usefulness of the second solution to the kleingordon equation of a. How to derive general solution to the kleingordon equation a. Pdf a universal quantum wave equation that yields dirac, kleingordon, schrodinger and quantum heat equations is derived. In what follows, we outline the derivation of kleingordon. We represent the scalar feynman propagator with the symbol d f x y.
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. Now, suppose a solution to the kleingordon equation is a free particle with energy eand momentum p ip ne x 11 1. Therefore, it is my goal to show how the earlier results of the purely real solutions could be applied when the. Schroeder, an introduction to quantum field theory this is a very clear and comprehensive book, covering everything in this course at the right level. The form of the klein gordon equation is derived by requiring that planewave solutions.
Derivation of solutions of the klein gordon equation from solutions of the wave equation volume 15 issue 2 ll. What is the lagrangian from which the kleingordon equation is derived in qft. Apr 12, 2016 how to derive general solution to the klein gordon equation. Nov 25, 2018 klein gordan equation,the klein gordon equation is derived. The nonrelativistic equation for the energy of a free particle is. Thus, in general, we will have to resort to an approximate procedure. Derivation of kleingordon equation in general relativity. The kleingordon equation kleinfockgordon equation or sometimes kleingordonfock equation is a relativistic wave equation, related to the schrodinger equation. Logical inference approach to relativistic quantum.
Classical applications of the kleingordon equation. It will also cover everything in the advanced quantum field theory course, much of the standard model course, and will serve you well if you go on to do research. The free complex kleingordon eld was discussed in lecture. Derivation of kleingordon equation from maxwells electric. As the field equations are developed, it is found that invariance of the scalar of curvature under the appropriate gauge and coordinate transformations implies the. Didactic derivation of the special theory of relativity from. As the field equations are developed, it is found that invariance of the scalar of curvature under the appropriate gauge and coordinate transformations implies the klein gordon equation. We consider three examples of vibrating systems whose mathematical descriptions lead to the kleingordon equation. Geometrical derivation of 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. I explained this in my lectures on introduction to quantum field theory and since i am not aware of a textbook treat ment of this material although all this is.
How to show that the feynman delta function satisfies the inhomogeneous kleingordon equation. Removing restriction to one dimension and rearranging, we recognize this as the klein gordon equation for a free particle. Derivation of solutions of the kleingordon equation from solutions of the wave 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. In what follows, we outline the derivation of klein gordon. The general solution to the kleingordon equation would then be given by. Later, the equation was revived and is now known as kleingordon equation.
The kleingordon equation is a linear homogeneous secondorder partial differential equation with constant coefficients. Derivation of einstein equation from maxwells equations and derivation of kleingordon equation where einstein energymomentum relation is derived from maxwells equations, and kleingordon equation is also derived from the same maxwells equation. It is shown that the kleingordon equation for a massive. Quantum mechanics of kleingordon equation katedra fyziky fjfi.
The schrodinger and kleingordon equations are directly derived from classical lagrangians. 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 kleingordon equation is applied in the description of mesons and corresponding fields. I had to use it for something, and afterwards i found myself thinking of its derivation. Since we want the lagrangian density to be invariant under lorentz transformations a linear wave equation, the lagrangian density can contain only the. Which propagator you have to use is welldefined by the physical problem at hand. The logical inference approach to quantum theory, proposed earlier ann. Derivation of einstein equation from maxwells equations and derivation of klein gordon equation where einstein energymomentum relation is derived from maxwells equations, and klein gordon equation is also derived from the same maxwells equation. Closely following the electromagnetic prototype of a wave equation, and attempting to describe the electron relativistically, he.
As we can see now, the apparent problems were manifestations of the new physics. The klein gordon equation is often written in natural units. For the reader not familiar with this equation, it is a relativistic wave equation related to. Aug 26, 2017 which propagator you have to use is welldefined by the physical problem at hand. Schrodinger himself formulated it earlier in his notes together with the schrodinger equation 51. Logical inference approach to relativistic quantum mechanics. So the klein gordon eld is physically and mathematically, too the simplest of the relativistic elds that one can study. I go over fourvector notation, fourgradient, and writing the equation in terms of the dalambertian.
The plane waves 10 are basic solutions and the field 9 is constructed by. Apr 25, 2016 the logical inference approach to quantum theory, proposed earlier ann. Subsequently, this studys focus is devoted for deriving. P r o bl em s w it h k lei n g o r do n e q ua t io n 1. It is shown that the klein gordon equation for a massive. We present a didactic derivation of the special theory of relativity in which lorentz transformations are discovered as symmetry transformations of the kleingordon equation.
Kleingordon eld is characterized by \particles with rest mass mand no other structure e. Deriving the klein gordon equation relativistic quantum. Since the terms required for invariance correspond with known quantum effects, no invariant classical limit is possible. The initial part of the derivation of the standard dirac equation, is a reformulation of the kleingordon, which is then augmented via the insertion of diracs gamma matrices, to account for both clockwise and anticlockwise spin, and for both positive and negative energy solutions. Proca equations the dirac equation predicts that the electron magnetic moment and its spin are related as 2 bs, while for normal. Relativistic wave equations and their derivation 5. How to obtain dirac equation from schrodinger equation and special relativity. So, none of the objections that led to discarding the klein equation held up with time. If you substitute the free particle solution into the kleingordon equation you get, unsurpisingly, the relation e 22p m. Kleingordon equation in schrodinger form 3 which is the usual relativistic formula for the energy of a particle. As the field equations are developed, it is found that invariance of the scalar of curvature under the appropriate gauge and coordinate transformations implies the kleingordon equation. Each of these components then satisfies a first order differential equation of time.
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