Spinor Decomposition of SU(2) Gauge Potential and The Spinor Structures of Chern-Simons and Chern Density

TL;DR

This paper explores the decomposition of SU(2) gauge potential using Pauli spinors, revealing spinor structures of topological invariants like Chern-Simons and Chern density, and relating knot quantum numbers to these structures.

Contribution

It introduces a novel spinor decomposition of SU(2) gauge potential and links it to topological invariants and knot quantum numbers in non-Abelian gauge theory.

Findings

Spinor structures of Chern-Simons form derived

Second Chern number characterized by Hopf indices

Knot quantum number linked to spinor structures

Abstract

In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor structures, the knot quantum number of non-Abelian gauge theory is discussed, and the second Chern number is characterized by the Hopf indices and the Brouwer degrees of $\phi $-mapping.