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

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.

27 pages, LaTeX, more details on self-adjoint extension (published version)

References in corpus (1)

• Feynman Propagator for a Free Scalar Field on a Causal Set

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• A Canonical Complex Structure and the Bosonic Signature Operator for Scalar Fields in Globally Hyperbolic Spacetimes
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