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Geometric spin foams, Yang-Mills theory and background-independent models (2005)
| Citations: | 8 - 2 self |
BibTeX
@MISC{Conrady05geometricspin,
author = {Florian Conrady},
title = {Geometric spin foams, Yang-Mills theory and background-independent models },
year = {2005}
}
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Abstract
We review the dual transformation from pure lattice gauge theory to spin foam models with an emphasis on a geometric viewpoint. This allows us to give a simple dual formulation of SU(N) Yang-Mills theory, where spin foam surfaces are weighted with the exponentiated area. In the case of gravity, we introduce a symmetry condition which demands that the amplitude of an individual spin foam depends only on its geometric properties and not on the lattice on which it is defined. For models that have this property, we define a new sum over abstract spin foams that is independent of any choice of lattice or triangulation. We show that a version of the Barrett-Crane model satisfies our symmetry requirement.
Keyphrases
yang-mills theory geometric spin foam background-independent model geometric viewpoint symmetry condition geometric property foam model individual spin foam pure lattice gauge theory simple dual formulation new sum abstract spin foam exponentiated area dual transformation symmetry requirement barrett-crane model spin foam surface
