The Fermionic Signature Operator and Quantum States in Rindler Space-Time

TL;DR

This paper constructs the fermionic signature operator in Rindler space-time, demonstrating its properties and relation to known quantum states like the Fulling-Rindler vacuum and Unruh state, and extends the construction to four dimensions.

Contribution

It introduces a covariant construction of quantum states using the fermionic signature operator in Rindler space-time, including new states in four dimensions.

Findings

Fermionic signature operator is self-adjoint on the solution space.

In 2D, it reproduces the Fulling-Rindler vacuum.

In 2D, it constructs the Unruh state and thermal states.

Abstract

The fermionic signature operator is constructed in Rindler space-time. It is shown to be an unbounded self-adjoint operator on the Hilbert space of solutions of the massive Dirac equation. In two-dimensional Rindler space-time, we prove that the resulting fermionic projector state coincides with the Fulling-Rindler vacuum. Moreover, the fermionic signature operator gives a covariant construction of general thermal states, in particular of the Unruh state. The fermionic signature operator is shown to be well-defined in asymptotically Rindler space-times. In four-dimensional Rindler space-time, our construction gives rise to new quantum states.