All Physics Faculty Publications

Document Type

Article

Journal/Book Title/Conference

Journal of Mathematical Physics

Volume

50

Issue

6

Publisher

American Institute of Physics

Publication Date

2009

First Page

062303-1

Last Page

062303-12

DOI

10.1063/1.3131678

Abstract

Given a group-invariant quasi-free state on the algebra of canonical commutation relations (CCR), we show how group averaging techniques can be used to obtain a symmetry-reduced CCR algebra and reduced quasi-free state. When the group is compact, this method of symmetry reduction leads to standard results which can be obtained using other methods. When the group is noncompact, the group averaging prescription relies on technically favorable conditions which we delineate. As an example, we consider symmetry reduction of the usual vacuum state for a Klein–Gordon field on Minkowski spacetime by a noncompact subgroup of the Poincaré group consisting of a 1-parameter family of boosts, a 1-parameter family of spatial translations and a set of discrete translations. We show that the symmetry-reduced CCR algebra and vacuum state correspond to that used by each of Berger, Husain, and Pierri for the polarized Gowdy T3 quantum gravity model.

Comments

Originally published by the American Institute of Physics. Publisher's PDF available through the Journal of Mathematical Physics.

http://arxiv.org/abs/0901.4293

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