Novel Topological Invariant in the U(1) Gauge Field Theory

TL;DR

This paper introduces new topological invariants in U(1) gauge field theory using decomposition and $\

Contribution

It presents novel topological invariants derived from gauge potential decomposition and $\

Findings

Defines a three-dimensional knot invariant.

Proposes a new four-dimensional topological invariant.

Links invariants to gauge field topology.

Abstract

Based on the decomposition of U(1) gauge potential theory and the $\phi$-mapping topological current theory, the three-dimensional knot invariant and a four-dimensional new topological invariant are discussed in the U(1) gauge field.