Kinematic projective quantum states for Loop Quantum Gravity coupled to tensor fields

TL;DR

This paper develops a method to construct kinematic quantum states for tensor field theories, extending Loop Quantum Gravity to include tensor fields using projective techniques.

Contribution

It introduces a novel construction of quantum states for tensor fields in LQG by applying Kijowski's projective techniques and builds upon Lanery and Thiemann's work.

Findings

Successfully constructs quantum states for LQG coupled with tensor fields.

Extends the framework of Loop Quantum Gravity to more complex matter couplings.

Provides a foundation for further quantum gravity research with tensor fields.

Abstract

We present a construction of kinematic quantum states for theories of tensor fields of an arbitrary sort. The construction is based on projective techniques by Kijowski. Applying projective quantum states for Loop Quantum Gravity obtained by Lanery and Thiemann we construct quantum states for LQG coupled to tensor fields.