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. We use consistency of Coulomb gauge condition to naturally deduce a new gauge condition. Furthermore, we obtain 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 is the sum of the orbital angular momentum and spin angular momentum of the non-Abelian gauge field. Finally, we obtain the anomalous fractional spin and discover that the fractional spin has the contributions of both the group superscript components and A0s(x) charge.
Highlights
Supersymmetric Chern-Simons systems have been investigated in some references[1,2,3]
One can observe that the partial angular momentum given by non-abelian Chern-Simons topological term is
Based on the global canonical Noether theorem, we deduce the angular momentum of this system and the partial angular momentum given by non-abelian Chern-Simons topological term
Summary
Supersymmetric Chern-Simons systems have been investigated in some references[1,2,3]. The conclusions are deserved to be discussed at quantum level by the phase-space path integral method, because the phase-space path integral method is more fundamental than the configuration-space path integral method It is the purpose of this paper to study the property of fractional spin of the SU(n) N=2 supersymmetric gauge field system with non-Abelian Chern-Simons topological term at the quantum field level.
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