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

TL;DR

This paper explores fermion coupling in spinfoam quantum gravity, establishing PCT symmetry, computing the Dirac determinant, and representing fermion correlation functions via Feynman diagrams on spinfoams.

Contribution

It introduces a PCT symmetry theorem for spinfoam fermions, provides new diagrammatic expansions for the Dirac determinant, and links fermion correlators to discretized Feynman diagrams on spinfoams.

Findings

PCT symmetry for spinfoam fermions proved

Explicit diagram expansions for Dirac determinant provided

Fermion correlation functions expressed as Feynman diagrams on spinfoams

Abstract

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.