A Loop Representation for the Quantum Maxwell Field

TL;DR

This paper develops a loop representation for the quantum Maxwell field, demonstrating its equivalence to Fock quantization and highlighting its potential applications in quantum optics, condensed matter physics, and quantum gravity.

Contribution

It introduces a loop-based quantization framework for the Maxwell field, connecting it to non-perturbative quantum gravity approaches and offering new insights into quantum geometry.

Findings

Loop representation is equivalent to Fock quantization for Maxwell field.

Framework may be useful in quantum optics and condensed matter physics.

Supports non-perturbative quantum gravity approaches.

Abstract

Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state methods, this framework may be useful in quantum optics. It is also well-suited for the discussion of issues related to flux quantization in condensed matter physics. Our own motivation, however, came from a non-perturbative approach to quantum gravity. The concrete results obtained in this paper for the Maxwell field provide independent support for that approach. In addition, they offer some insight into the physical interpretation of the mathematical structures that play, within this approach, an essential role in the description of the quantum geometry at Planck scale.