Misplaced Pages

Dirac equation in curved spacetime

Article snapshot taken from[REDACTED] with creative commons attribution-sharealike license. Give it a read and then ask your questions in the chat. We can research this topic together.

Math Formula Information

Formula: i γ a e a μ D μ Ψ = m Ψ {\displaystyle \mathrm {i} \gamma ^{a}e_{a}^{\mu }D_{\mu }\Psi =m\Psi }

Name: Dirac equation in curved spacetime

Description: generalization of the Dirac equation from Minkowski space to a general Lorentzian manifold with spin structure

Elements of the Formula

Gamma matrices γ {\displaystyle \gamma } matrix representation of a Clifford algebra
Dirac spinor field Ψ {\displaystyle \Psi } field whose values are Dirac spinors
Dirac operator D {\displaystyle D} first-order differential linear operator on spinor bundle, whose square is the Laplacian
rest mass (invariant mass) or rest energy m {\displaystyle m} body's intrinsic mass (or equivalent intrinsic energy), motion-independent (Lorentz invariant); equals total mass (or energy) when at rest
imaginary unit i {\displaystyle \mathrm {i} } square root of negative one, used to define complex numbers
frame field in general relativity e {\displaystyle e} Spacetime modeled by four pointwise-orthonormal vector fields

Data Source

https://www.wikidata.org/Special:EntityPage/Q16853908

Dirac equation in curved spacetime Add topic