Igor Khavkine

Date of Award


Degree Type


Degree Name

Doctor of Philosophy


Applied Mathematics


Dr. J. Daniel Christensen


The focus of this thesis is the study of spin foam models of quantum gravity on a computer. These models include the standard Barrett-Crane (BC) spin foam model, as well as the new Engle-Pereira-Rovelli (EPR) and Freidel-Krasnov (FK) models. New numerical algorithms are developed and implemented, based on the existing Christensen-Egan (CE) algorithm, to allow computations with the BC model in the presence of a cosmological constant (implemented through q-deformation) and to allow computations with the recently proposed EPR and FK models.

For the first time, we show that the inclusion of a positive cosmological constant, a long standing open problem for spin foams, curiously changes the behavior of the BC model, rendering the expectation values of its observables discontinuous in the limit of zero cosmological constant. Also, unlike previous work, this investigation was carried out on large triangulations, which are closer to large semiclassical space-times.

Efficient numerical algorithms are described and implemented, for the first time, allowing the evaluation of the EPR and FK spin foam vertex amplitudes. An initial application of these algorithms is the study of the effective single vertex large spin asymptotics of the new models. Their asymptotic behavior is found to be qualitatively similar to that of the BC model. The leading asymptotic behavior does not exhibit the oscillatory character expected by analogy with the Ponzano-Regge model.

Two important tests of the spin foam semiclassical limit are wave packet prop­ agation and evaluation of the graviton propagator matrix elements. These tests are generalized to encompass the three major spin foam models. The wave packet prop­ agation test is carried out in greater generality than previously. The results indicate that conjectures about good semiclassical behavior of the new spin foam models may have been premature.



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