Dirac equation in curved spacetime

Math Formula Information

Formula: ${\displaystyle \mathrm {i} \gamma ^{a}e_{a}^{\mu }D_{\mu }\Psi =m\Psi }$

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

Data Source

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