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

June 13, 2016

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.

open access link
J. Math. Anal. Appl. 454 (2017) 385-411

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%%% add \usepackage[utf8]{inputenc} to your latex preamble
@article{Finster:2016apv,
author = "Finster, Felix and Murro, Simone and Röken, Christian",
title = "{The Fermionic Signature Operator and Quantum States in
Rindler Space-Time}",
journal = "J. Math. Anal. Appl.",
volume = "454",
year = "2017",
pages = "385-411",
doi = "10.1016/j.jmaa.2017.04.044",
eprint = "1606.03882",
archivePrefix = "arXiv",
primaryClass = "math-ph",
SLACcitation = "%%CITATION = ARXIV:1606.03882;%%"
}

Keywords:

Hadamard state, KMS states, Rindler Spacetime, Fermionic Signature Operator, massive Dirac equation