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

Felix Finster, Simone Murro, Christian Röken
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
%%% contains utf-8, see: http://inspirehep.net/info/faq/general#utf8 %%% 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