Faddeev-Senjanovic Quantization of SU(n) N=2 Supersymmetric Gauge Field System with Non-Abelian Chern-Simons Topological Term and Its Fractional Spin

TL;DR

This paper applies Faddeev-Senjanovic path integral quantization to an SU(n) N=2 supersymmetric gauge system with a non-abelian Chern-Simons term, deriving fractional spin and analyzing angular momentum contributions.

Contribution

It introduces a novel quantization approach for this supersymmetric gauge system and reveals the fractional spin contributions from gauge components and charges.

Findings

Derived the generating functional of Green functions in phase space.

Calculated the fractional spin of the system.

Identified contributions to total angular momentum from gauge fields and charges.

Abstract

Using Faddeev-Senjanovic path integral quantization for constrained Hamilton system, we quantize SU(n) N=2 supersymmetric gauge field system with non-abelian Chern-Simons topological term in 2+1 dimensions, and use consistency of a gauge condition naturally to deduce another gauge condition. Further, we get the generating functional of Green function in phase space, deduce the angular momentum based on the global canonical Noether theorem at quantum level, obtain the fractional spin of this supersymmetric system, and show that the total angular momentum has the orbital angular momentum and spin angular momentum of the non-abelian gauge field. Finally, we find out the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and the A_0^s (x) charge.