Quantum 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: Schrödinger representation with unitary dynamics

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

doi:10.1103/physrevd.76.124031

Cited by 66 publications

(117 citation statements)

References 27 publications

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“…If this were so, the quantum theory presented here would be essentially unique, once the choice of internal time and fundamental field has been fixed. This issue will be the subject of a future investigation [32].…”

Section: Conclusion and Further Commentsmentioning

confidence: 99%

Quantum GowdyT3model: A unitary description

2006

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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, so that both the Schrödinger 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.

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Section: Conclusion and Further Commentsmentioning

confidence: 99%

Quantum GowdyT3model: A unitary description

2006

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“…The requirement of axisymmetry restricts the harmonics in this expansion to the set {Y l0 , l ∈ N}, the only spherical harmonics which are independent of φ. The coefficients of ξ in this expansion in harmonics satisfy an equation identical to (19), except for the substitution of n by l + 1 2 and the redefinition of the function f (t), whose role is played now byf (t) := f (t) − 1/4. From this point on, the discussion is completely parallel to that presented for the field on the circle, with the only caveat that the mode numbers n correspond now to positive half-integers, l + 1 2 , rather than to positive integers, a fact which, nonetheless, does not affect the computations nor the rationale of our analysis.…”

Section: Fock Quantization Of the Modelmentioning

confidence: 99%

“…By considering the counterpart of J 0 on the canonical phase space Γ (rather than on S), one can construct the functional representation which is unitarily equivalent to the J 0 -Fock description (see [19] for a detailed treatment in complex variables and [20] for the GNS relationship between Schrödinger and Fock representations). The result is a Schrödinger representation of the canonical commutation relations on the Hilbert space H = L 2 (Q, µ) of square integrable functions on the infinite dimensional linear space Q = {(q n , x n ); n ∈ N + } ∼ = (R 2 ) N + , with respect to the Gaussian measure…”

Section: Quantum Representationmentioning

confidence: 99%

Uniqueness of the Fock quantization of a free scalar field onS1with time dependent mass

et al. 2009

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We analyze the quantum description of a free scalar field on the circle in the presence of an explicitly time dependent potential, also interpretable as a time dependent mass. Classically, the field satisfies a linear wave equation of the formξ − ξ ′′ + f (t)ξ = 0. We prove that the representation of the canonical commutation relations corresponding to the particular case of a massless free field (f = 0) provides a unitary implementation of the dynamics for sufficiently general mass terms, f (t). Furthermore, this representation is uniquely specified, among the class of representations determined by S 1 -invariant complex structures, as the only one allowing a unitary dynamics. These conclusions can be extended in fact to fields on the two-sphere possessing axial symmetry. This generalizes a uniqueness result previously obtained in the context of the quantum field description of the Gowdy cosmologies, in the case of linear polarization and for any of the possible topologies of the spatial sections.

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“…In both cases, the complex structure that would be natural if the field were massless allows for a unitary quantum implementation of the field dynamics and, besides, shares the symmetry of the spatial sections of the auxiliary spacetime (which the vacuum state inherits). In fact, these two properties select a unique unitary equivalence class of Fock representations: all the representations with these attributes are unitarily equivalent [16][17][18]. Furthermore, if we change the field description by performing a linear canonical transformation that scales the field by a time-dependent factor, unitarity is lost: there is no Fock representation for the new canonical pair of field variables in which dynamics is represented in terms of a unitary operator [19].…”

Section: Introductionmentioning

confidence: 99%

Unique Fock quantization of scalar cosmological perturbations

et al. 2012

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We investigate the ambiguities in the Fock quantization of the scalar perturbations of a FriedmannLemaître-Robertson-Walker model with a massive scalar field as matter content. We consider the case of compact spatial sections (thus avoiding infrared divergences), with the topology of a threesphere. After expanding the perturbations in series of eigenfunctions of the Laplace-Beltrami operator, the Hamiltonian of the system is written up to quadratic order in them. We fix the gauge of the local degrees of freedom in two different ways, reaching in both cases the same qualitative results. A canonical transformation, which includes the scaling of the matter field perturbations by the scale factor of the geometry, is performed in order to arrive at a convenient formulation of the system. We then study the quantization of these perturbations in the classical background determined by the homogeneous variables. Based on previous work, we introduce a Fock representation for the perturbations in which: (a) the complex structure is invariant under the isometries of the spatial sections and (b) the field dynamics is implemented as a unitary operator. These two properties select not only a unique unitary equivalence class of representations, but also a preferred field description, picking up a canonical pair of field variables among all those that can be obtained by means of a time-dependent scaling of the matter field (completed into a linear canonical transformation). Finally, we present an equivalent quantization constructed in terms of gauge-invariant quantities. We prove that this quantization can be attained by a mode-by-mode time-dependent linear canonical transformation which admits a unitary implementation, so that it is also uniquely determined.PACS numbers: 98.80. Qc, 04.62.+v, 98.80.Cq

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Quantum GowdyT3model: Schrödinger representation with unitary dynamics

Cited by 66 publications

References 27 publications

Quantum GowdyT3model: A unitary description

Quantum GowdyT3model: A unitary description

Uniqueness of the Fock quantization of a free scalar field onS1with time dependent mass

Unique Fock quantization of scalar cosmological perturbations

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