Manifestly Causal In-In Perturbation Theory about the Interacting Vacuum

Matthew Baumgart; Raman Sundrum

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arXiv · 2010.10785

Manifestly Causal In-In Perturbation Theory about the Interacting Vacuum

Matthew Baumgart·Raman Sundrum

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Abstract

In-In perturbation theory is a vital tool for cosmology and nonequilibrium physics. Here, we reconcile an apparent conflict between two of its important aspects with particular relevance to De Sitter/inflationary contexts: (i) the need to slightly deform unitary time evolution with an i*epsilon prescription that projects the free ("Bunch-Davies") vacuum onto the interacting vacuum and renders vertex integrals well-defined, and (ii) Weinberg's "nested commutator" reformulation of in-in perturbation theory which makes manifest the constraints of causality within expectation values of local operators, assuming exact unitarity. We show that a modified i*epsilon prescription maintains the exact unitarity on which the derivation of (ii) rests, while nontrivially agreeing with (i) to all orders of perturbation theory.

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Matthew Baumgart, Raman Sundrum. 2020-10-21. Manifestly Causal In-In Perturbation Theory about the Interacting Vacuum. https://arxiv.org/abs/2010.10785

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