After an introduction to (2+1)-dimensional gravity, the non-trivial topologies approach is discussed in both the first-order (connection) and second-order (metric) formalisms. The classical solutions for g=1, the torus, are discussed and shown to be related by a time-dependent canonical transformation. Their relative quantisations are compared and shown to differ by terms of $(\hbar^3)$.
Exact Quantisation of 2+1 Gravity on the torus
NELSON, Jeanette Ethel
1996-01-01
Abstract
After an introduction to (2+1)-dimensional gravity, the non-trivial topologies approach is discussed in both the first-order (connection) and second-order (metric) formalisms. The classical solutions for g=1, the torus, are discussed and shown to be related by a time-dependent canonical transformation. Their relative quantisations are compared and shown to differ by terms of $(\hbar^3)$.
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