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Journal Article

Holonomy Spin Foam Models: Definition and Coarse Graining

MPS-Authors
http://pubman.mpdl.mpg.de/cone/persons/resource/persons4344

Bahr,  Benjamin
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons20705

Dittrich,  Bianca
Canonical and Covariant Dynamics of Quantum Gravity, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

http://pubman.mpdl.mpg.de/cone/persons/resource/persons45866

Hellmann,  Frank
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Fulltext (public)

1208.3388
(Preprint), 393KB

PRD87_044048.pdf
(Any fulltext), 546KB

Supplementary Material (public)
There is no public supplementary material available
Citation

Bahr, B., Dittrich, B., Hellmann, F., & Kaminski, W. (2013). Holonomy Spin Foam Models: Definition and Coarse Graining. Physical Review D, 87(4): 044048. doi:10.1103/PhysRevD.87.044048.


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-E981-4
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.