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Free keywords:
General Relativity and Quantum Cosmology, gr-qc,High Energy Physics - Lattice, hep-lat,High Energy Physics - Theory, hep-th
Abstract:
We propose a new holonomy formulation for spin foams, which naturally extends
the theory space of lattice gauge theories. This allows current spin foam
models to be defined on arbitrary two-complexes as well as to generalize
current spin foam models to arbitrary, in particular finite groups. The
similarity with standard lattice gauge theories allows to apply standard coarse
graining methods, which for finite groups can now be easily considered
numerically. We will summarize other holonomy and spin network formulations of
spin foams and group field theories and explain how the different
representations arise through variable transformations in the partition
function. A companion paper will provide a description of boundary Hilbert
spaces as well as a canonical dynamic encoded in transfer operators.
