Hadamard property of the in and out states for Dirac fields on asymptotically static spacetimes

TL;DR

This paper proves that for Dirac fields on asymptotically static spacetimes, the in and out states exist, are asymptotic vacua, and satisfy the Hadamard condition, ensuring well-behaved quantum states.

Contribution

It establishes the existence and Hadamard property of in/out states for Dirac fields on asymptotically static spacetimes, extending quantum field theory in curved spacetime.

Findings

Existence of in/out states for Dirac fields.

In/out states are asymptotic vacuum states.

In/out states satisfy the Hadamard condition.

Abstract

We consider massive Dirac equations on asymptotically static spacetimes with a Cauchy surface of bounded geometry. We prove that the associated quantized Dirac field admits in and out states, which are asymptotic vacuum states when some time coordinate tends to $\mp\infty$. We also show that the in /out states are Hadamard states.(new version with some typos corrected).