We construct a 4d Lorentzian spin foam model capable of describing both spacelike and
timelike surfaces. To do so we use a coherent state approach inspired by the Riemannian
FK model. Using the coherent state method we reproduce the results of the EPRL model
for Euclidean tetrahedra and extend the model to include Lorentzian tetrahedra. The
coherent states of spacelike/timelike triangles are found to correspond to elements of the
discrete/continuous series of SU(1,1). It is found that the area spectrum of both spacelike
and timelike surfaces is quantized. A path integral for the quantum theory is defined
as a product of vertex amplitudes. The states corresponding to timelike triangles are
constructed in a basis diagonalised with respect to a noncompact generator. A derivation
of the matrix elements of the generators of SL(2,C) in this basis is provided.
| Identifer | oai:union.ndltd.org:WATERLOO/oai:uwspace.uwaterloo.ca:10012/5593 |
| Date | January 2010 |
| Creators | Hnybida, Jeffrey |
| Source Sets | University of Waterloo Electronic Theses Repository |
| Language | English |
| Detected Language | English |
| Type | Thesis or Dissertation |
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