Simplicial group field theory

Tuesday, May 2nd
Marco Finocchiaro, Albert Einstein Institute
Title: Simplicial Group Field Theory models for Euclidean quantum gravity: recent developments 
PDF of the talk (2M)
Audio+Slides [.mp4 15MB]

by Jorge Pullin, Louisiana State University

The approach to quantum gravity known as “spin foams” is based on the quantization technique known as the path integral. In this technique probabilities are assigned for a given slice of space to transition to a future slice in a space-time. Since in loop quantum gravity spatial slices are associated to spin networks, as these evolve in time transitioning to slices of the future one gets the “spin foams”. Group field theory is a technique in which an ordinary (but non-local) quantum field theory is constructed in such a way that its Feynman diagrams yield the probabilities of the spin foam approach. There is an analogue en 1+1 dimensions known as “matrix models” that were widely studied in the 1990’s. Group field theories can be viewed as their generalization to four dimensions.

 Formulating spin foams in terms of group field theories has several advantages. Results do not depend on the triangulations picked, as one expects it should be but is not obvious in terms of spin foams. One can import techniques from field theories, in particular to introduce notions of renormalizability and a continuum limit.

 In this talk a particular group field theory model is presented and discussed in some detail. In particular a numerical analysis of the resulting probabilities was made. And results were compared to a popular model of spin foams, the EPRL model. Certain insights on the possible choices in the construction of the model and how it could influence the ultraviolet behavior and possible singularities present were discussed.