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

Atsushi Higuchi; William Couto Correa De Lima

doi:10.1103/PhysRevD.101.065009

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

Atsushi Higuchi, William Couto Correa De Lima

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	065009
Number of pages	12
Journal	Physical Review D - Particles, Fields, Gravitation and Cosmology
Volume	101
DOIs	https://doi.org/10.1103/PhysRevD.101.065009
Publication status	Published - 17 Mar 2020

Bibliographical note

This is an author-produced version of the published paper. Uploaded in accordance with the publisher’s self-archiving policy. Further copying may not be permitted; contact the publisher for details.

Keywords

Perturbation theory
Quantum fields in curved spacetime
Unruh effect

Access to Document

10.1103/PhysRevD.101.065009

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Cite this

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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.",

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KW - Perturbation theory

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