Quantum Gowdy $T^3$ model: A unitary description

TL;DR

This paper presents a detailed quantization of Gowdy T^3 spacetimes, demonstrating a unitary quantum evolution by transforming the system into a static background with a time-dependent potential, improving upon previous non-unitary approaches.

Contribution

It introduces a canonical transformation that achieves a unitary quantum evolution for the Gowdy T^3 model, addressing prior issues with non-unitarity in quantum gravity.

Findings

Quantum evolution is shown to be unitary.

A canonical transformation simplifies the model.

Implications for quantum gravity and field theory in curved spacetime.

Abstract

The quantization of the family of linearly polarized Gowdy $T^3$ spacetimes is discussed in detail, starting with a canonical analysis in which the true degrees of freedom are described by a scalar field that satisfies a Klein-Gordon type equation in a fiducial time dependent background. A time dependent canonical transformation, which amounts to a change of the basic (scalar) field of the model, brings the system to a description in terms of a Klein-Gordon equation on a background that is now static, although subject to a time dependent potential. The system is quantized by means of a natural choice of annihilation and creation operators. The quantum time evolution is considered and shown to be unitary, allowing both the Schr\"odinger and Heisenberg pictures to be consistently constructed. This has to be contrasted with previous treatments for which time evolution failed to be implementable as a unitary transformation. Possible implications for both canonical quantum gravity and quantum field theory in curved spacetime are commented.