Aspects of plane wave (matrix) string dynamics

We consider the quantization of scalar fields in spacetimes such that, by means of a suitable scaling of the field by a time dependent function, the field equation can be regarded as that of a field with a time dependent mass propagating in an auxiliary ultrastatic static background. For Klein-Gordon fields, it is well known that there exist an infinite number of nonequivalent Fock representations of the canonical commutation relations and, therefore, of inequivalent quantum theories. A context in which this kind of ambiguities arises and prevents the derivation of robust results is, e.g., in the quantum analysis of cosmological perturbations. In these situations, typically, a suitable scaling of the field by a time dependent function leads to a description in an auxiliary static background, though the nonstationarity still shows up in a time dependent mass. For such a field description, and assuming the compactness of the spatial sections, we recently proved in three or less spatial dimensions that the criteria of a natural implementation of the spatial symmetries and of a unitary time evolution are able to select a unique class of unitarily equivalent vacua, and hence of Fock representations. In this work, we succeed to extend our uniqueness result to the consideration of all possible field descriptions that can be reached by a time dependent canonical transformation which, in particular, involves a scaling of the field by a function of time. This kind of canonical transformations modify the dynamics of the system and introduce a further ambiguity in its quantum description, exceeding the choice of a Fock representation. Remarkably, for any compact spatial manifold in less than four dimensions, we show that our criteria eliminate any possible nontrivial scaling of the field other than that leading to the description in an auxiliary static background. Besides, we show that either no time dependent redefinition of the field momentum is allowed or, if this may happen -something which is typically the case only for one-dimensional spatial manifolds-, the redefinition does not introduce any Fock representation that cannot be obtained by a unitary transformation.

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“…Remarkably, our results were recently found useful also in the context of string dynamics in arbitrary plane wave backgrounds[36].…”

mentioning

confidence: 52%

“…In addition, in Sec. V we show that either there is no freedom to include a time dependent linear contribution of the field in the momentum or, if the freedom exists (something that may 3 Remarkably, our results were recently found useful also in the context of string dynamics in arbitrary plane wave backgrounds [36].…”

Section: Introductionmentioning

confidence: 66%

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

et al. 2012

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“…Let us return to the field equation (15) and decompose the field χ into eigenmodes of the LB operator:…”

Section: The Model: Free Fields In De Sitter Spacetimementioning

confidence: 99%

“…Although rather simple at first glance, these results find application in a variety of situations, including the quantization of inhomogeneous spacetimes, such as the Gowdy models (see [7][8][9][10][11][12]), the quantization of cosmological perturbations [2,13,14] and the discussion of string dynamics in arbitrary plane wave backgrounds [15]. Another particular instance in which these results can be applied is the case of free fields in a nonstationary spacetime which is nevertheless conformal to a static universe, by means of a time-dependent conformal factor.…”

Section: Introductionmentioning

confidence: 99%

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

Cortez¹,

Blas²,

Marugán³

et al. 2013

Class. Quantum Grav.

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We prove that, under the standard conformal scaling, a free scalar field in de Sitter spacetime admits an O(4)-invariant Fock quantization such that time evolution is unitarily implemented. Since this applies in particular to the massless case, this result disproves previous claims in the literature. We discuss the relationship between this quantization with unitary dynamics and the family of O(4)-invariant Hadamard states given by Allen and Folacci, as well as with the Bunch-Davies vacuum.

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“…Thus, one expects any modified theory of gravity to accommodate such solutions. They are also of great interest in other areas of theoretical physics such as string theory, see, e.g., [44] and references therein. Here, we present a set of massless and massive exact gravitational pp-wave solutions.…”

Section: Introductionmentioning

confidence: 99%

Gravitational waves in ghost free bimetric gravity

Mohseni¹

2012

J. Cosmol. Astropart. Phys.

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We obtain a set of exact gravitational wave solutions for the ghost free bimetric theory of gravity. With a flat reference metric, the theory admits the vacuum Brinkmann plane wave solution for suitable choices of the coefficients of different terms in the interaction potential. An exact gravitational wave solution corresponding to a massive scalar mode is also admitted for arbitrary choice of the coefficients with the reference metric being proportional to the spacetime metric. The proportionality factor and the speed of the wave are calculated in terms of the parameters of the theory. We also show that a F (R) extension of the theory admits similar solutions but in general is plagued with ghost instabilities.

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Aspects of plane wave (matrix) string dynamics

Cited by 4 publications

References 63 publications

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

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

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

Gravitational waves in ghost free bimetric gravity

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