Editing Relativistic wave equations (section)

{{Short description|Wave equations respecting special and general relativity}}
{{Redirect|Relativistic quantum field equations|related concepts|Relativistic quantum mechanics|and|Schrödinger field}}
{{Quantum mechanics|cTopic=Equations}}
{{quantum field theory}}

In [[physics]], specifically [[relativistic quantum mechanics]] (RQM) and its applications to [[particle physics]], '''relativistic wave equations''' predict the behavior of [[particles]] at high [[energy|energies]] and [[velocity|velocities]] comparable to the [[speed of light]]. In the context of [[quantum field theory]] (QFT), the equations determine the dynamics of [[quantum field]]s.
The solutions to the equations, universally denoted as {{math|ψ}} or {{math|Ψ}} ([[Greek language|Greek]] [[Psi (letter)|psi]]), are referred to as "[[wave function]]s" in the context of RQM, and "[[field (physics)|field]]s" in the context of QFT. The equations themselves are called "wave equations" or "field equations", because they have the mathematical form of a [[wave equation]] or are generated from a [[Lagrangian density]] and the field-theoretic [[Euler–Lagrange equation]]s (see [[classical field theory]] for background).

In the [[Schrödinger picture]], the wave function or field is the solution to the [[Schrödinger equation]],
<math display="block">
 i\hbar\frac{\partial}{\partial t}\psi = \hat{H} \psi,
</math>
one of the [[Mathematical formulation of quantum mechanics#Pictures of dynamics|postulates of quantum mechanics]]. All relativistic wave equations can be constructed by specifying various forms of the [[Hamiltonian (quantum mechanics)|Hamiltonian operator]] ''Ĥ'' describing the [[Physical system|quantum system]]. Alternatively, [[Richard Feynman|Feynman]]'s [[path integral formulation]] uses a Lagrangian rather than a Hamiltonian operator.

More generally – the modern formalism behind relativistic wave equations is [[Lorentz group]] theory, wherein the spin of the particle has a correspondence with the [[representations of the Lorentz group]].<ref name="T Jaroszewicz, P.S Kurzepa">
{{cite journal
 |author1=T Jaroszewicz |author2=P.S Kurzepa | year = 1992
 | title = Geometry of spacetime propagation of spinning particles 
 | journal = Annals of Physics
 |volume=216 |issue=2 |pages=226–267 | doi=10.1016/0003-4916(92)90176-M
 |bibcode=1992AnPhy.216..226J
}}</ref>