Wilson loops, geometric operators and fermions in 3d group field theory

Details Wilson loops, geometric operators and fermions in 3d group field theory Wilson loops, geometric operators and fermions in 3d group field theory

2009-11-12

arxiv.org/abs/0911.2391v1

Central Eur.J.Phys.9:1043-1056,2011

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

13 pages, many figures, uses psfrag

Scientific paper

10.2478/s11534-010-0137-2

Group field theories whose Feynman diagrams describe 3d gravity with a varying configuration of Wilson loop observables and 3d gravity with volume observables at each vertex are defined. The volume observables are created by the usual spin network grasping operators which require the introduction of vector fields on the group. We then use this to define group field theories that give a previously defined spin foam model for fermion fields coupled to gravity, and the simpler quenched approximation, by using tensor fields on the group. The group field theory naturally includes the sum over fermionic loops at each order of the perturbation theory.

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