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 iϵ 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 iϵ prescription maintains the exact unitarity on which the derivation of (ii) rests, while nontrivially agreeing with (i) to all orders of perturbation theory.
Highlights
We fleshed the argument out into a complete formal derivation of eq (1.2) in the appendix of [1]
In-In perturbation theory is a vital tool for cosmology and nonequilibrium physics
We show that a modified i prescription maintains the exact unitarity on which the derivation of (ii) rests, while nontrivially agreeing with (i) to all orders of perturbation theory
Summary
We fleshed the argument out into a complete formal derivation of eq (1.2) in the appendix of [1]. This completes the proof of the equivalence of perturbative diagrams that connect to the correlator time twhether we use propagators G from eq (2.3) or GU from eq (2.6).
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