Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions

Details Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions Spinfoam Fermions: PCT Symmetry, Dirac Determinant, and Correlation Functions

2011-01-17

arxiv.org/abs/1101.3264v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

26 pages, 9 figures

Scientific paper

We discuss fermion coupling in the framework of spinfoam quantum gravity. We analyze the gravity-fermion spinfoam model and its fermion correlation functions. We show that there is a spinfoam analog of PCT symmetry for the fermion fields on spinfoam model, where a PCT theorem is proved for spinfoam fermion correlation functions. We compute the determinant of the Dirac operator for the fermions, where two presentations of the Dirac determinant are given in terms of diagram expansions. We compute the fermion correlation functions and show that they can be given by Feynman diagrams on the spinfoams, where the Feynman propagators can be represented by a discretized path integral of a world-line action along the edges of the underlying 2-complex.

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