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Title: Functional evolution of quantum cylindrical waves
Authors: Cho, Demian H.J.
Varadarajan, Madhavan
Issue Date: 21-Nov-2006
Publisher: The Institute of Physics Publishing
Citation: Classical and Quantum Gravity, 2006, Vol.23, p6115-6140
Abstract: Kuchar showed that the quantum dynamics of (one polarization) cylindrical wave solutions to vacuum general relativity is determined by those of a free axially symmetric scalar field along arbitrary axially symmetric foliations of a fixed flat (2 + 1)-dimensional spacetime. We investigate if such a dynamics can be defined unitarily within the standard Fock space quantization of the scalar field. Evolution between two arbitrary slices of an arbitrary foliation of the flat spacetime can be built out of a restricted class of evolutions (and their inverses). The restricted evolution is from an initial flat slice to an arbitrary (in general, curved) slice of the flat spacetime and can be decomposed into (i) 'time' evolution in which the spatial Minkowskian coordinates serve as spatial coordinates on the initial and the final slice, followed by (ii) the action of a spatial diffeomorphism of the final slice on the data obtained from (i). We show that although the functional evolution of (i) is unitarily implemented in the quantum theory, generic spatial diffeomorphisms of (ii) are not. Our results imply that a Tomanaga–Schwinger type functional evolution of quantum cylindrical waves is not a viable concept even though, remarkably, the more limited notion of functional evolution in Kuchar's 'half-parametrized formalism' is well defined.
Description: Restricted Access. An open access version is available at
ISSN: 0264-9381
1361-6382 (Online)
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Copyright: (2006) by the Institute of Physics
Appears in Collections:Research Papers (TP)

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