A 4d Lorentzian Spin Foam Model With Timelike Surfaces
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Date
2010-10-07T18:19:40Z
Authors
Hnybida, Jeffrey
Journal Title
Journal ISSN
Volume Title
Publisher
University of Waterloo
Abstract
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.
Description
Keywords
Quantum Gravity, Spin Foam