Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields

TL;DR

This paper investigates the conditions for unitary evolution in quantum Gowdy models with S^1 x S^2 and S^3 topologies, showing that suitable field redefinitions enable unitarity in Fock quantizations.

Contribution

It demonstrates that unitarity in these models can be achieved through specific field redefinitions based on conformal factors, and establishes the equivalence of different Fock quantizations.

Findings

No initial Fock quantization admits unitary evolution without redefinition.

Field redefinitions based on conformal factors restore unitarity.

Fock quantizations with SO(3) symmetry are unitarily equivalent.

Abstract

The purpose of this paper is to study in detail the problem of defining unitary evolution for linearly polarized S^1 x S^2 and S^3 Gowdy models (in vacuum or coupled to massless scalar fields). We show that in the Fock quantizations of these systems no choice of acceptable complex structure leads to a unitary evolution for the original variables. Nonetheless, unitarity can be recovered by suitable redefinitions of the basic fields. These are dictated by the time dependent conformal factors that appear in the description of the standard deparameterized form of these models as field theories in certain curved backgrounds. We also show the unitary equivalence of the Fock quantizations obtained from the SO(3)-symmetric complex structures for which the dynamics is unitarily implemented.