- Relativistic wave equations
Before the creation of
quantum field theory , physicists attempted to formulate versions of theSchrödinger equation which were compatible withspecial relativity . Such equations are called relativistic wave equations.The first such equation was discovered by
Erwin Schrödinger himself; however, he realized that this equation, now called theKlein-Gordon equation , gave incorrect results when used to calculate the energy levels of hydrogen. Schrödinger discarded his relativistic wave equation, only to realize a few months later that its non-relativistic limit (what is now called theSchrödinger equation ) was still of importance.List of relativistic wave equations
The following list of relativistic wave equations is categorised by the spin of the particles they describe.
pin 0
*
Klein-Gordon equation : describes a massless or massive spin-0 particle (such asHiggs boson s)
::left(Box^2 + left(frac{mc}{hbar} ight)^2 ight) psi = 0pin 1/2
*
Weyl equation : describes massless spin-1/2 particles
*Dirac equation : describes massive spin-1/2 particles (such aselectron s)::left( i hbar gamma^mu partial_mu - m c ight) psi = 0
*Majorana equation : describes a massiveMajorana particle
::i hbar {partial!!!ig /} psi - m c psi_c = 0 qquad qquad
*Breit equation : describes two massive spin-1/2 particles (such aselectron s) interacting electromagnetically to first order in perturbation theorypin 1
*
Maxwell equations : describe aphoton (massless spin-1 particle)
*Proca equation : describes a massive spin-1 particle (such asW and Z bosons )
::partial_mu(partial^mu A^ u - partial^ u A^mu)+left(frac{mc}{hbar} ight)^2 A^ u=0Gauge fields
* Yang-Mills equation: describes a non-abelian gauge field
*Yang-Mills-Higgs equation : describes a non-abelian gauge field coupled with a massive spin-0 particle
*Kemmer equation : an alternative equation for spin-1 particlespin 3/2
*
Rarita-Schwinger equation : describes a massive spin-3/2 particle
::epsilon^{mu u ho sigma} gamma^5 gamma_ u partial_ ho psi_sigma + mpsi^mu = 0pin 2
*
Einstein field equations : describe interaction of matter with thegravitational field (massless spin-2 field).
::R_{ab} - {1 over 2}R g_{ab} = -{8 pi} T_{ab}+ Lambda g_{ab}.Arbitrary spin
*
Bargmann-Wigner equations : describe free particles of arbitrary integral or half-integral spinAll the particle equations except the Breit, the Yang-Mills, Yang-Mills-Higgs and Einstein are
linear .ee also
*
Special relativity
*Status of special relativity
*Lorentz transformations
*Quantum Field Theory
*Scalar field theory
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