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Title

Unitary evolution as a uniqueness criterion

AuthorsCortez, Jerónimo; Mena Marugán, Guillermo A. ; Olmedo, Javier ; Velhinho, José M.
Issue Date2015
PublisherWorld Scientific Publishing
CitationProceedings of the MG13 Meeting on General Relativity: 2272- 2274 (2015)
AbstractIt is well known that the process of quantizing field theories is plagued with ambiguities. First, there is ambiguity in the choice of basic variables describing the system. Second, once a choice of field variables has been made, there is ambiguity concerning the selection of a quantum representation of the corresponding canonical commutation relations. The natural strategy to remove these ambiguities is to demand positivity of energy and to invoke symmetries, namely by requiring that classical symmetries become unitarily implemented in the quantum realm. The success of this strategy depends, however, on the existence of a sufficiently large group of symmetries, usually including time-translation invariance. These criteria are therefore generally insufficient in non-stationary situations, as is typical for free fields in curved spacetimes. Recently, the criterion of unitary implementation of the dynamics has been proposed in order to select a unique quantization in the context of manifestly non-stationary systems. Specifically, the unitarity criterion, together with the requirement of invariance under spatial symmetries, has been successfully employed to remove the ambiguities in the quantization of linearly polarized Gowdy models as well as in the quantization of a scalar field with time varying mass, propagating in a static background whose spatial topology is either of a d-sphere (with d = 1, 2, 3) or a three torus. Following Ref. 3, we will see here that the symmetry and unitarity criteria allows for a complete removal of the ambiguities in the quantization of scalar fields propagating in static spacetimes with compact spatial sections, obeying field equations with an explicitly time-dependent mass, of the form These results apply in particular to free fields in spacetimes which, like e.g. in the closed FRW models, are conformal to a static spacetime, by means of an exclusively time-dependent conformal factor. In fact, in such cases the free field equation can be mapped to an equation of the above type, via a suitable scaling of the field…
DescriptionProceedings of the MG13 Meeting on General Relativity Stockholm University, Sweden, 1 – 7 July 2012; PARALLEL SESSIONS: Loop Quantum Gravity: Cosmology and Black Holes
Publisher version (URL)http://dx.doi.org/10.1142/9789814623995_0417
URIhttp://hdl.handle.net/10261/138254
DOI10.1142/9789814623995_0417
Identifiersdoi: 10.1142/9789814623995_0417
isbn: 978-981-4612-14-2
Appears in Collections:(CFMAC-IEM) Libros y partes de libros
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