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 2-complexes as well as to generalize current spin foam models to arbitrary, in particular, finite groups. The similarity with standard lattice gauge theories allows us 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.
5 More- Received 15 November 2012
DOI:https://doi.org/10.1103/PhysRevD.87.044048
© 2013 American Physical Society