FROM DIMENSIONAL REDUCTION OF 4d SPIN FOAM MODEL TO ADDING NON-GRAVITATIONAL FIELDS TO 3d SPIN FOAM MODEL

A Kaluza–Klein-like approach for a 4d spin foam model is considered. By applying this approach to a model based on group field theory in 4d (TOCY model), and using the Peter–Weyl expansion of the gravitational field, reconstruction of new non-gravitational fields and interactions in the action are found. The perturbative expansion of the partition function produces graphs colored with SU(2) algebraic data, from which one can reconstruct a 3d simplicial complex representing space-time and its geometry (like in the Ponzano–Regge formulation of pure 3d quantum gravity), as well as the Feynman graph for typical matter fields. Thus a mechanism for generation of matter and construction of new dimensions are found from pure gravity.

MEASUREMENTS AND INFORMATION IN SPIN FOAM MODELS

In the three-dimensional spin foam model of quantum gravity with a cosmological constant, there exists a set of observables associated with spin network graphs. A set of probabilities is calculated from these observables, and hence the associated Shannon entropy can be defined. We present the Shannon entropy associated with these observables and find some interesting bounded inequalities. The problem relates measurements, entropy and information theory in a simple way which we explain.