Kinematics of arbitrary spin matter fields in loop quantum gravity

TL;DR

This paper explores the kinematical aspects of matter fields with arbitrary spin in loop quantum gravity, focusing on their coupling, symmetry properties, and implications of quantum constraints.

Contribution

It introduces a framework for analyzing arbitrary spin matter fields within loop quantum gravity, including extensions to electromagnetic fields and higher spin classical actions.

Findings

Defined a less ambiguous variant of Baez-Krasnov path observables

Analyzed symmetry properties of spin network states under diffeomorphism averaging

Discussed extensions to electromagnetic fields and higher spin matter excitations

Abstract

Loop quantum gravity envisions a small scale structure of spacetime that is markedly different from that of the classical spacetime continuum. This has ramifications for the excitation of matter fields and for their coupling to gravity. There is a general understanding of how to formulate scalar fields, spin $\frac{1}{2}$ fields and gauge fields in the framework of loop quantum gravity. The goal of the present work is to investigate kinematical aspects of this coupling. We will study implications of the Gau{\ss} and diffeomorphism constraint for the quantum theory: We define and study a less ambiguous variant of the Baez-Krasnov path observables, and investigate symmetry properties of spin network states imposed by diffeomorphism group averaging. We will do this in a setting which allows for matter excitations of spin $\frac{1}{2}$ and higher. In the case of spin $\frac{1}{2}$, we will also discuss extensions of it by introducing an electromagnetic field and antiparticles. We finally discuss in how far the picture with matter excitations of higher spin can be obtained from classical actions for higher spin fields.