The phase space of 2+1 gravity
In recent years there has been a resurgence of interest in 2+1 gravity and there have been claims that 2+1 gravity is quantizable. In order to understand and evaluate these claims the classical phase space on which quantization is attempted must be understood. This thesis is an attempt to underst...
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| Format: | Others |
| Language: | English |
| Published: |
2009
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| Online Access: | http://hdl.handle.net/2429/4183 |
| Summary: | In recent years there has been a resurgence of interest in 2+1 gravity and there have been
claims that 2+1 gravity is quantizable. In order to understand and evaluate these claims
the classical phase space on which quantization is attempted must be understood. This
thesis is an attempt to understand the phase space of 2+1 gravity in terms of physical
models. We write the action of 2+1 gravity in the connection formalism entirely in terms
of the holonomies of a genus g surface. We apply this formulation to the genus one and
two surfaces. We analyze the structure of the genus two constrained configuration space
in detail to show that it consists of five disconnected components. Relating our results
to a more mathematical analysis we show that only two of these regions are physically
relevant and these two are identified with one another. Finally, we discuss the phase
space of the genus one and two surfaces including the effect of large diffeomorphisms.
We conclude that the theory does not lead to a well defined quantization. === Science, Faculty of === Physics and Astronomy, Department of === Graduate |
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