Dirac equation in non-Riemannian geometries

Abstract

We present the Dirac equation in a geometry with torsion and non-metricity balancing generality and simplicity as much as possible. In doing so, we use the vielbein formalism and the Clifford algebra. We also use an index-free formalism which allows us to construct objects that are totally invariant. It turns out that the previous apparatuses not only make possible a simple deduction of the Dirac equation but also allow us to exhibit some details that is generally obscure in the literature.

13 pages; one reference added

References in corpus (3)

• Status of non-Riemannian cosmology
• Geometrization of electromagnetism in tetrad-spin-connection gravity
• Dirac equation in spacetimes with torsion and non-metricity

Cited by in corpus (5)

• Teleparallel Palatini theories
• Observable traces of non-metricity: new constraints on metric-affine gravity
• Minimal coupling in presence of non-metricity and torsion
• Projective symmetries and induced electromagnetism in metric-affine gravity
• Inconsistencies of nonmetric Einstein-Dirac-Maxwell theories and a cure for geometric flows of f(Q) black ellipsoid, toroid and wormhole solutions