Quantum Gowdy $T^3$ model: A uniqueness result

Abstract

Modulo a homogeneous degree of freedom and a global constraint, the linearly polarised Gowdy $T^3$ cosmologies are equivalent to a free scalar field propagating in a fixed nonstationary background. Recently, a new field parameterisation was proposed for the metric of the Gowdy spacetimes such that the associated scalar field evolves in a flat background in 1+1 dimensions with the spatial topology of $S^1$, although subject to a time dependent potential. Introducing a suitable Fock quantisation for this scalar field, a quantum theory was constructed for the Gowdy model in which the dynamics is implemented as a unitary transformation. A question that was left open is whether one might adopt a different, nonequivalent Fock representation by selecting a distinct complex structure. The present work proves that the chosen Fock quantisation is in fact unique (up to unitary equivalence) if one demands unitary implementation of the dynamics and invariance under the group of constant $S^1$ translations. These translations are precisely those generated by the global constraint that remains on the Gowdy model. It is also shown that the proof of uniqueness in the choice of complex structure can be applied to more general field dynamics than that corresponding to the Gowdy cosmologies.

28 pages, minor changes, version accepted for publication in Classical and Quantum Gravity

References in corpus (14)

• Background Independent Quantum Gravity: A Status Report
• Uniqueness of diffeomorphism invariant states on holonomy-flux algebras
• Quantum Gowdy $T^3$ model: A unitary description
• Canonical Quantization of the Gowdy Model
• On the Relation Between Fock and Schroedinger Representations for a Scalar Field
• Unitary evolution in Gowdy cosmology
• Quantum Dynamics of the Polarized Gowdy Model
• Probing Quantum General Relativity Through Exactly Soluble Midi-Superspaces II: Polarized Gowdy Models
• Midi-superspace Models of Canonical Quantum Gravity
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• Feasibility of a Unitary Quantum Dynamics in the Gowdy $T^3$ Cosmological Model
• On Unitary Time Evolution in Gowdy $T^3$ Cosmologies
• Physical Properties of Quantum Field Theory Measures
• Functional evolution of quantum cylindrical waves

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