Uniqueness of the Fock quantization of the Gowdy<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>T</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:math>model

Cortez, Jerónimo; Marugán, Guillermo A. Mena; Velhinho, José M.

doi:10.1103/physrevd.75.084027

Cited by 69 publications

(130 citation statements)

References 29 publications

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“…IV B). Moreover, as we mentioned in the introduction, much stronger results have indeed been proven regarding the uniqueness of the quantization [6,9].…”

Section: B Fock Quantizationmentioning

confidence: 91%

“…The field is completely determined by , by P : lnp and by their respective momentum and configuration (canonically) conjugate variables, P and Q (see Ref. [6] for details). Therefore, all local degrees of freedom reside in the field .…”

Section: A the Classical Modelmentioning

confidence: 99%

“…These functionals are square integrable with respect to a Gaussian measure with covariance ÿB=2. 6 On the Hilbert space defined in this way, the basic operators of configuration and momentum are…”

Section: A General Frameworkmentioning

confidence: 99%

“…In this case, not only is the evolution unitary and the gauge group naturally implemented, but also it has been shown that any other Fock quantization of the new field with such properties is unitarily equivalent to the constructed one [6 -9]. Furthermore, the adopted field parametrization turns out to be unique in a precise sense under the condition of the existence of a Fock representation (FR) with an invariant unitary action of the gauge group and a unitary dynamics [6]. These results were mainly formulated in the language of Fock space, which is natural from the perspective of a scalar field in a fixed background.…”

Section: Introductionmentioning

confidence: 99%

“…However, this proposal for the choice of fundamental field has the undesirable property of not implementing the dynamics (generated by the internal notion of time) unitarily. Actually, although this lack of unitarity was first proven [5] for a ''natural quantization'' of the associated scalar field, introduced by Pierri [4], it has been recently shown that there exists no Fock quantization with a unitary dynamics, at least if one also demands an invariant unitary implementation of the gauge group that remains on the model after gauge fixing [6]. To solve this problem, a new field parametrization, together with an essentially unique quantum representation, was recently introduced.…”

Section: Introductionmentioning

confidence: 99%

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Quantum GowdyT3model: Schrödinger representation with unitary dynamics

et al. 2007

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The linearly polarized Gowdy T 3 model is paradigmatic for studying technical and conceptual issues in the quest for a quantum theory of gravity since, after a suitable and almost complete gauge fixing, it becomes an exactly soluble midisuperspace model. Recently, a new quantization of the model, possessing desired features such as a unitary implementation of the gauge group and of the time evolution, has been put forward and proven to be essentially unique. An appropriate setting for making contact with other approaches to canonical quantum gravity is provided by the Schrödinger representation, where states are functionals on the configuration space of the theory. Here we construct this functional description, analyze the time evolution in this context and show that it is also unitary when restricted to physical states, i.e. states which are solutions to the remaining constraint of the theory.

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“…IV B). Moreover, as we mentioned in the introduction, much stronger results have indeed been proven regarding the uniqueness of the quantization [6,9].…”

Section: B Fock Quantizationmentioning

confidence: 91%

Section: A the Classical Modelmentioning

confidence: 99%

Section: A General Frameworkmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Quantum GowdyT3model: Schrödinger representation with unitary dynamics

et al. 2007

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Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization and Approximated Solutions

Blas

Martín-Benito

Marugán

2013

Springer Proceedings in Mathematics &Amp; Statistics

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Quantum unitary dynamics in cosmological spacetimes

2015

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a b s t r a c tWe address the question of unitary implementation of the dynamics for scalar fields in cosmological scenarios. Together with invariance under spatial isometries, the requirement of a unitary evolution singles out a rescaling of the scalar field and a unitary equivalence class of Fock representations for the associated canonical commutation relations. Moreover, this criterion provides as well a privileged quantization for the unscaled field, even though the associated dynamics is not unitarily implementable in that case. We discuss the relation between the initial data that determine the Fock representations in the rescaled and unscaled descriptions, and clarify that the S-matrix is well defined in both cases. In our discussion, we also comment on a recently proposed generalized notion of unitary implementation of the dynamics, making clear the difference with the standard unitarity criterion and showing that the two approaches are not equivalent.

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Uniqueness of the Fock quantization of the GowdyT3model

Cited by 69 publications

References 29 publications

Quantum GowdyT3model: Schrödinger representation with unitary dynamics

Quantum GowdyT3model: Schrödinger representation with unitary dynamics

Inhomogeneous Loop Quantum Cosmology: Hybrid Quantization and Approximated Solutions

Quantum unitary dynamics in cosmological spacetimes

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