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

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 Schrödinger 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.

Cited by in corpus (13)

• 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: A uniqueness result
• Quantum Gowdy $T^3$ Model: Schrodinger Representation with Unitary Dynamics
• The time-dependent quantum harmonic oscillator revisited: Applications to Quantum Field Theory
• Quantum unitary evolution of linearly polarized S^1\times S^2 and S^3 Gowdy models coupled to massless scalar fields
• Uniqueness of the Fock representation of the Gowdy $S^1\times S^2$ and $S^3$ models
• 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
• Evolution Operators for Linearly Polarized Two-Killing Cosmological Models
• 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