Vector and Spinor Decomposition of SU(2) Gauge Potential, their quivalence and Knot Structure in SU(2) Chern-Simons Theory

TL;DR

This paper explores the decomposition and equivalence of SU(2) gauge potentials, derives a related nonlinear sigma model, and discusses the knot structure in SU(2) Chern-Simons theory using topological current theory.

Contribution

It introduces a novel decomposition and equivalence of SU(2) gauge potentials, connects to a nonlinear sigma model, and analyzes knot structures via topological methods.

Findings

Established the equivalence of spinor and vector decompositions of SU(2) gauge potential.

Derived the Faddeev nonlinear O(3) sigma model action from massive SU(2) gauge theory.

Analyzed knot structures in SU(2) Chern-Simons theory using topological charge characterized by Hopf indices and Brouwer degrees.

Abstract

In this paper, spinor and vector decomposition of SU(2) gauge potential are presented and their equivalence is constructed using a simply proposal. We also obtain the action of Faddeev nonlinear O(3) sigma model from the SU(2) massive gauge field theory which is proposed according to the gauge invariant principle. At last, the knot structure in SU(2) Chern-Simons filed theory is discussed in terms of the $\phi$--mapping topological current theory. The topological charge of the knot is characterized by the Hopf indices and the Brouwer degrees of $\phi$-mapping.