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 (2)

• Quantum Gowdy $T^3$ model: A unitary description
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics

Cited by in corpus (11)

• Hybrid Quantum Gowdy Cosmology: Combining Loop and Fock Quantizations
• Uniqueness of the Fock quantization of the Gowdy $T^3$ model
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Uniqueness of the Fock representation of the Gowdy $S^1\times S^2$ and $S^3$ models
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Loop Quantization of Polarized Gowdy Model on $T^3$: Kinematical States and Constraint Operators
• Loop Quantization of Polarized Gowdy Model on $T^3$: Classical Theory
• Hamiltonian Dynamics of Linearly Polarized Gowdy Models Coupled to Massless Scalar Fields
• Unitary evolution of free massless fields in de Sitter space-time
• Schrodinger quantization of linearly polarized Gowdy $S^1\times S^2$ and $S^3$ models coupled to massless scalar fields