Relativistic wave equations

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Before the creation of quantum field theory, physicists attempted to formulate versions of the Schrödinger equation which were compatible with special 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 the Klein-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 nonrelativistic limit (what is now called the Schrödinger equation) was still of importance.

[edit] List of relativistic wave equations

Klein-Gordon equation: describes a massless or massive spin-0 particle (such as Higgs bosons)

$(\Box^2 + (\frac{mc}{\hbar})^2) \psi = 0$

Weyl equation: describes a massless spin-1/2 particle
Dirac equation: describes a massive spin-1/2 particule (such as electrons)

$i \hbar \gamma^\mu \partial_\mu \psi - m c \psi = 0 \,$

Majorana equation: describes a massive Majorana particle

$i \hbar {\partial\!\!\!\big /} \psi - m c \psi_c = 0 \qquad \qquad$

Breit equation: describes two massive spin-1/2 particles (such as electrons) interacting electromagnetically to first order in perturbation theory
Maxwell equations: describe a photon (massless spin-1 particle)
Proca equation: describes a massive spin-1 particle (such as W and Z bosons)

$\partial_\mu(\partial^\mu A^\nu - \partial^\nu A^\mu)+\left(\frac{mc}{\hbar}\right)^2 A^\nu=0$

Kemmer equation: an alternative equation for spin-1 particles
Rarita-Schwinger equation: describes a massive spin-3/2 particle

$\epsilon^{\mu \nu \rho \sigma} \gamma^5 \gamma_\nu \partial_\rho \psi_\sigma + m\psi^\mu = 0$

Bargmann-Wigner equations: describe free particles of arbitrary integral or half-integral spin
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
Einstein field equations: describe interaction of matter with the gravitational field (massless spin-2 field).