Conformal mapping of Unruh temperature

Abstract

Thanks to a local interpetation of the KMS condition, the mapping from (unbounded) wedge regions of Minkowski space-time to (bounded) double-cone regions is extended to the Unruh temperature associated to relevant observers in both regions. A previous result, the diamond's temperature, is shown to be proportional to the inverse of the conformal factor (Weyl rescaling of the metric) of this map. One thus explains from a mathematical point of view why an observer with finite lifetime experiences the vacuum as a thermal state whatever his acceleration, even vanishing.

Paper shortened and reorganized. To be published in Modern Physics Letters A

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• Equivalence of the Hawking temperature in conformal frames
• Entanglement Degradation in Causal Diamonds
• Light Cone Black Holes
• Spectral Properties of the Symmetry Generators of Conformal Quantum Mechanics: A Path-Integral Approach
• Lorentzian fermionic action by twisting euclidean spectral triples
• A Modular Operator Approach to Entanglement of Causally Closed Regions
• Conformal quantum mechanics of causal diamonds: Time evolution, thermality, and instability via path integral functionals
• Path integral derivation of the thermofield double state in causal diamonds
• On temperature of a diamond
• Twisting Noncommutative Geometries with Applications to High Energy Physics
• Emergence of time in quantum gravity: is time necessarily flowing ?