Taming the alpha-vacuum

TL;DR

This paper addresses the non-renormalizability of scalar field theories in de Sitter space with alpha-vacua by proposing a new propagator and time-ordering, ensuring causality and renormalizability at one loop.

Contribution

It introduces a novel propagator and generalized time-ordering for alpha-vacua, resolving divergences and establishing causality and renormalizability.

Findings

A new propagator based on generalized time-ordering avoids interference divergences.

The proposed framework is causal and renormalizable at one loop for a broad class of antipodal interactions.

The approach extends the understanding of quantum fields in de Sitter space with alpha-vacua.

Abstract

An interacting scalar field theory in de Sitter space is non-renormalizable for a generic alpha-vacuum state. This pathology arises since the usual propagator used allows for a constructive interference among propagators in loop corrections, which produces divergences that are not proportional to standard counterterms. This interference can be avoided by defining a new propagator for the alpha-vacuum based on a generalized time-ordering prescription. The generating functional associated with this propagator contains a source that couples to the field both at a point and at its antipode. To one loop order, we show that a set of theories with very general antipodal interactions is causal and renormalizable.