Photon inner product and the Gauss linking number

TL;DR

This paper explores the relationship between self-duality, loop representation, and knot invariants in quantum Maxwell theory, revealing that the inner product measure relates to the Gauss linking number of loops.

Contribution

It demonstrates that in the loop representation of quantum Maxwell fields, the inner product measure can be expressed through the Gauss linking number, connecting quantum field theory with knot invariants.

Findings

Inner product measure relates to Gauss linking number

Loop representation uses self-dual connections

Links between quantum theory and knot invariants established

Abstract

It is shown that there is an interesting interplay between self-duality, loop representation and knots invariants in the quantum theory of Maxwell fields in Minkowski space-time. Specifically, in the loop representation based on self-dual connections, the measure that dictates the inner product can be expressed as the Gauss linking number of thickened loops.