Equivalence between the in-in perturbation theories for quantum fields in Minkowski spacetime and in the Rindler wedge

Abstract

We investigate the relation between the time-ordered vacuum correlation functions for interacting real scalar fields in Minkowski spacetime and in the Rindler wedge. The correlation functions are constructed perturbatively within the in-in formalism, often employed in calculations in more general spacetimes. We prove to all orders in perturbation theory that the time-ordered vacuum correlation functions can be calculated in the in-in formalism with internal vertices restricted to any Rindler wedge containing the external points. This implies that the Minkowski in-in (or in-out) perturbative expansion of the vacuum correlation functions is reproduced by the Rindler in-in perturbative expansion of these correlators in a thermal state at the Unruh temperature.

arXiv comment12 pages, 3 figures. Minor corrections; matches the published version

References in corpus (6)

• Quantum Chromodynamics and Other Field Theories on the Light Cone
• The Unruh effect and its applications
• Decay of accelerated protons and the existence of the Fulling-Davies-Unruh effect
• On the Equivalence between Euclidean and In-In Formalisms in de Sitter QFT
• Decay of protons and neutrons induced by acceleration
• The Unruh effect for mixing neutrinos

Cited by in corpus (3)

• Isometry invariance of exact correlation functions in various charts of Minkowski and de Sitter spaces
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• Hartle-Hawking state in the real-time formalism