Jeronimo Cortez

Quantum Gowdy T3 model: a unitary description

The quantization of the family of linearly polarized Gowdy T{sup 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, so that both the Schroedinger and Heisenberg pictures can 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 noted.

ON UNITARY TIME EVOLUTION IN GOWDY T3 COSMOLOGIES

A non-perturbative canonical quantization of the Gowdy T3 polarized models is considered here. This approach profits from the equivalence between the symmetry reduced model and 2 + 1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is made, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a two-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the corresponding Hilbert space of quantum states. The implications of this result for both the quantization of fields on curved manifolds and other physically relevant questions regarding the initial singularity are discussed.

A uniqueness criterion for the Fock quantization of scalar fields with time-dependent mass

A major problem in the quantization of fields in curved spacetimes is the ambiguity in the choice of a Fock representation for the canonical commutation relations. There exists infinite number of choices leading to different physical predictions. In stationary scenarios, a common strategy is to select a vacuum (or a family of unitarily equivalent vacua) by requiring invariance under the spacetime symmetries. When stationarity is lost, a natural generalization consists in replacing time invariance by unitarity in the evolution. We prove that when the spatial sections are compact, the criterion of a unitary dynamics, together with the invariance under the spatial isometries, suffices to select a unique family of Fock quantizations for a scalar field with time-dependent mass.

Unitary evolution in Gowdy cosmology

Recent results on the nonunitary character of quantum time evolution in the family of Gowdy

Uniqueness of the Fock quantization of scalar fields in spatially flat cosmological spacetimes

{T}^{3}

Schrödinger and Fock representation for a field theory on curved spacetime

spacetimes bring the question of whether one should abandon the most sacred principle of unitary evolution in cosmology. In this work we show that the answer is in the negative. We put forward a full nonperturbative canonical quantization of the polarized Gowdy

Criteria for the determination of time dependent scalings in the Fock quantization of scalar fields with a time dependent mass in ultrastatic spacetimes

{T}^{3}

Uniqueness of the Fock quantization of fields with unitary dynamics in nonstationary spacetimes

model that implements the dynamics while preserving unitarity. We discuss possible implications of this result.

Fock quantization of a scalar field with time dependent mass on the three-sphere: Unitarity and uniqueness

We study the Fock quantization of scalar fields in (generically) time dependent scenarios, focusing on the case in which the field propagation occurs in –either a background or effective– spacetime with spatial sections of flat compact topology. The discussion finds important applications in cosmology, like e.g. in the description of test Klein-Gordon fields and scalar perturbations in Friedmann-Robertson-Walker spacetime in the observationally favored flat case. Two types of ambiguities in the quantization are analyzed. First, the infinite ambiguity existing in the choice of a Fock representation for the canonical commutation relations, understandable as the freedom in the choice of inequivalent vacua for a given field. Besides, in cosmological situations, it is customary to scale the fields by time dependent functions, which absorb part of the evolution arising from the spacetime, which is treated classically. This leads to an additional ambiguity, this time in the choice of a canonical pair of field variables. We show that both types of ambiguities are removed by the requirements of (a) invariance of the vacuum under the symmetries of the three-torus, and (b) unitary implementation of the dynamics in the quantum theory. In this way, one arrives at a unique class of unitarily equivalent Fock quantizations for the system. This result provides considerable robustness to the quantum predictions and renders meaningful the confrontation with observation.

Massless scalar field in de Sitter spacetime: unitary quantum time evolution

Linear free field theories are one of the few Quantum Field Theories that are exactly soluble. There are, however, (at least) two very different languages to describe them, Fock space methods and the Schroedinger functional description. In this paper, the precise sense in which the two representations are related is reviewed. Several properties of these representations are studied, among them the well known fact that the Schroedinger counterpart of the usual Fock representation is described by a Gaussian measure. A real scalar field theory is considered, both on Minkowski spacetime for arbitrary, non-inertial embeddings of the Cauchy surface, and for arbitrary (globally hyperbolic) curved spacetimes. As a concrete example, the Schroedinger representation on stationary and homogeneous cosmological spacetimes is constructed.