The phase space of 2+1 gravity

• Main Author: Fugleberg, Todd Darwin
• Language: English
• Published: 2009
• Online Access: http://hdl.handle.net/2429/4183

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.