Spin foams with timelike surfaces

Details Spin foams with timelike surfaces Spin foams with timelike surfaces

2010-03-29

arxiv.org/abs/1003.5652v2

Class. Quant. Grav.27:155014, 2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, no figures; v2: remarks on operator formalism added in discussion; correction: the spin 1/2 irrep of the discrete se

Scientific paper

10.1088/0264-9381/27/15/155014

Spin foams of 4d gravity were recently extended from complexes with purely spacelike surfaces to complexes that also contain timelike surfaces. In this article, we express the associated partition function in terms of vertex amplitudes and integrals over coherent states. The coherent states are characterized by unit 3--vectors which represent normals to surfaces and lie either in the 2--sphere or the 2d hyperboloids. In the case of timelike surfaces, a new type of coherent state is used and the associated completeness relation is derived. It is also shown that the quantum simplicity constraints can be deduced by three different methods: by weak imposition of the constraints, by restriction of coherent state bases and by the master constraint.

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