Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics

TL;DR

This paper constructs a Schrödinger representation for the quantum Gowdy T^3 model, demonstrating that the unitary evolution of physical states is maintained, thus providing a bridge to other quantum gravity approaches.

Contribution

It develops a Schrödinger functional representation for the quantum Gowdy T^3 model with unitary dynamics, connecting it to broader quantum gravity frameworks.

Findings

The Schrödinger representation for the model is explicitly constructed.

Time evolution remains unitary when restricted to physical states.

The approach facilitates comparison with other canonical quantum gravity methods.

Abstract

The linearly polarized Gowdy $T^3$ model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble midisuperspace model. Recently, a new quantization of the model, possessing desired features such as a unitary implementation of the gauge group and of the time evolution, has been put forward and proven to be essentially unique. An appropriate setting for making contact with other approaches to canonical quantum gravity is provided by the Schr\"odinger representation, where states are functionals on the configuration space of the theory. Here we construct this functional description, analyze the time evolution in this context and show that it is also unitary when restricted to physical states, i.e. states which are solutions to the remaining constraint of the theory.