Deformed Wong Particles

TL;DR

This paper generalizes the Lorentz force law to particles with complex internal degrees of freedom, revealing how quantum group symmetries can break gauge invariance and affect field definitions.

Contribution

It introduces equations of motion for particles with non-closed algebraic internal degrees of freedom and analyzes their impact on gauge invariance and field tensor definitions.

Findings

Coupling $SU_q(2)$ particles to $SU(2)$ fields breaks gauge invariance to $U(1)$.

Internal degrees of freedom do not always generate finite algebras.

The antisymmetric field tensor may not be globally definable when sourced by such particles.

Abstract

By generalizing the Feynman proof of the Lorentz force law, recently reported by Dyson, we derive equations of motion for particles possessing internal degrees of freedom $I^a$ which do not, in general, generate a finite algebra. We obtain consistency criteria for fields which interact with such particles. It is argued that when a particle with internal $SU_q(2)$ degrees of freedom is coupled to $SU(2)$ gauge fields, $SU(2)$ gauge invariance is broken to $U(1)$. We further claim that when such an $SU_q(2)$ particle acts as a source for the field theory, the second rank antisymmetric field tensor, in general, cannot be globally defined.