Fermionic one-particle states in curved spacetimes

TL;DR

This paper demonstrates the existence of a one-particle and vacuum state for spin-1/2 fields in general curved spacetimes, showing that propagating modes are localized and resemble those in two-dimensional Minkowski space, enabling a second quantization interpretation.

Contribution

It introduces a framework for defining one-particle states and vacua for fermions in curved spacetimes, extending concepts from flat spacetime quantum field theory.

Findings

Feynman propagator resembles that of chiral fermions in 2D Minkowski space

Propagating modes are localized on 2D subspaces

A notion of vacuum state exists in general curved backgrounds for spin 1/2 fields

Abstract

We show that a notion of one-particle state and the corresponding vacuum state exists in general curved backgrounds for spin $\frac{1}{2}$ fields. A curved spacetime can be equipped with a coordinate system in which the metric component $g_{--}=0$. We separate the component of the left-handed massless Dirac field which is annihilated by the null vector $\partial_-$ and compute the corresponding Feynman propagator. We find that the propagating modes are localized on two dimensional subspaces and the Feynman propagator is similar to the Feynman propagator of chiral fermions in two dimensional Minkowski spacetime. Therefore, it can be interpreted in terms of one-particle states and the corresponding vacuum state similarly to the second quantization in Minkowski spacetime.