Anomalies, boundaries and the in-in formalism

TL;DR

This paper proposes using the in-in formalism for anomaly calculations in quantum field theory, introduces new results related to boundary value problems, and corrects a heat-kernel coefficient, offering a novel perspective on anomalies.

Contribution

It introduces the in-in formalism as a new framework for anomaly calculations and provides novel results for boundary value problems and heat-kernel coefficients.

Findings

In-in formalism provides a new perspective for anomaly calculations.

New results for anomalies in boundary value problems.

A correction to the $a_5$ heat-kernel coefficient.

Abstract

In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting for anomaly calculations is the `in-in', or closed-time path formulation of quantum field theory. There are also some new results for anomalies in the context of boundary value problems, and a new correction to the $a_5$ heat-kernel coefficient.