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arXiv · 1606.03882

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

Felix Finster·Simone Murro·Christian Röken
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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.

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Felix Finster, Simone Murro, Christian Röken. 2016-06-13. The Fermionic Signature Operator and Quantum States in Rindler Space-Time. https://doi.org/10.1016/j.jmaa.2017.04.044

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