Non-Unitarity Problem in Quantum Gravity Corrections to Quantum Field Theory with Born-Oppenheimer Approximation

TL;DR

This paper addresses the non-unitarity issue in quantum gravity corrections to quantum field theory by proposing a new WKB expansion method using kinematical action as a clock, restoring unitarity.

Contribution

It introduces a novel WKB expansion approach with kinematical action to achieve unitary evolution in quantum gravity corrections.

Findings

Previous methods exhibited non-unitary evolution due to quantum gravity effects.

The new approach successfully recovers unitary dynamics in the semiclassical limit.

The method clarifies the role of the clock variable in quantum gravity corrections.

Abstract

The problem of time is one of the most relevant open issues in canonical quantum gravity. Although there is a huge literature about this topic, a commonly accepted solution has not been found yet. Here, we focus on the semiclassical approach to the problem of time, that has the main goal of reproducing quantum field theory on a fixed WKB background accounting also for quantum gravity corrections. We analyze the different choices of the expansion parameter and discuss the problems arising in previous proposals, where a non-unitary evolution emerges as an effect of quantum gravity corrections. In this work we develop a new approach to solve this problem by performing the WKB expansion with the introduction of the so-called kinematical action as a clock for quantum matter, that allows to recover a unitary dynamics.