Abstract
variational derivation of the Dirac equation for a spin-half field on a curved background.
The action considered contains three key terms:
The minimally coupled Dirac term.
A scalar curvature coupling term.
A Hermitian derivative coupling to the Riemann tensor.
The derivation details all necessary foundational assumptions, including metric compatibility, spinorial compatibility, antisymmetry of the spin connection, and the contracted Bianchi identity. Every step in the variational calculation is explicitly shown, which includes integration by parts and statements about boundary terms. The final equation of motion is derived in manifestly covariant form.
Supplementary materials
Title
Curvature coupled dirac dynamics in curved spacetime
Description
variational derivation of the Dirac equation for a spin-half field on a curved background.
The action considered contains three key terms:
The minimally coupled Dirac term.
A scalar curvature coupling term.
A Hermitian derivative coupling to the Riemann tensor.
The derivation details all necessary foundational assumptions, including metric compatibility, spinorial compatibility, antisymmetry of the spin connection, and the contracted Bianchi identity. Every step in the variational calculation is explicitly shown, which includes integration by parts and statements about boundary terms. The final equation of motion is derived in manifestly covariant form.
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