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Title: Topics in 2 + 1 gravity and conformal field theory
Author: Johnson, Richard Gunn
ISNI:       0000 0004 2690 8703
Awarding Body: University of Nottingham
Current Institution: University of Nottingham
Date of Award: 2009
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We study the Hamiltonian dynamics for a system of two colliding point particles coupled to (2+1)-dimensional gravity with a negative cosmological constant by anchoring the dynamics of the system to its spatial infinity. We reduce the Chern-Simons formulation of the gravitational action, finding the reduced Hamiltonian for three special cases of the particle masses, in a phase space chart coordinatised by the geodesic distance between the two particles and its conjugate momentum. The dimension of the reduced phase space is two. At the threshold of black hole formation, the black hole mass depends linearly on the momentum, in agreement with previous analysis in a holonomy-based phase space chart. We use the reduced action to compute the semiclassical probability amplitude of two particles to tunnel out of the black hole, finding that the imaginary part of the action is equal to the Bekenstein-Hawking entropy of the hole. We also study the form that conformal field theory (CFT) correlation functions take in coset spaces of (2, C). We realise the (2, C) twistor space T in two distinct but equivalent ways, deriving some important facts about this space, and we also give one representation of another coset space B. We examine the form of CFT correlation functions in T, B and two other related spaces using techniques from representation theory and make a number of comments on the twistor transform for T.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QC170 Atomic physics. Constitution and properties of matter ; QC Physics