Quantization of Dirac fields in static spacetime

TL;DR

This paper analyzes the Hamiltonian structure of Dirac fields in static spacetimes, deriving explicit solutions and constructing the quantum field operator using positive and negative energy splits.

Contribution

It provides explicit expressions for fundamental solutions and propagators, and formalizes the quantum field construction in static spacetimes.

Findings

Explicit fundamental solutions derived

Propagator expressed in terms of Hamiltonian

Quantum field operator constructed from energy split

Abstract

On a static spacetime, the solutions of the Dirac equation are generated by a time-independent Hamiltonian. We study this Hamiltonian and characterize the split into positive and negative energy. We use it to find explicit expressions for advanced and retarded fundamental solutions and for the propagator. Finally, we use a fermion Fock space based on the positive/negative energy split to define a Dirac quantum field operator whose commutator is the propagator.