Diffeomorphism invariant subspaces in Witten's 2 + 1 quantum gravity on
- 1 November 1995
- journal article
- Published by IOP Publishing in Classical and Quantum Gravity
- Vol. 12 (11) , 2735-2745
- https://doi.org/10.1088/0264-9381/12/11/006
Abstract
We address the role of large diffeomorphisms in Witten's 2 + 1 gravity on the manifold . In a `spacelike sector' quantum theory that treats the large diffeomorphisms as a symmetry, rather than as gauge, the Hilbert space is shown to contain no non-trivial finite-dimensional subspaces that are invariant under the large diffeomorphisms. Infinite-dimensional closed invariant subspaces are explicitly constructed, and the representation of the large diffeomorphisms is thus shown to be reducible. Comparison is made to Witten's theory on , where is a higher genus surface.Keywords
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