Interaction via reduction and nonlinear superconformal symmetry

TL;DR

This paper demonstrates how reducing a free spin-1/2 particle system under specific constraints yields a superconformal mechanics model with coupled bosonic and fermionic degrees of freedom, revealing quantum corrections and nonlinear symmetry structures.

Contribution

It introduces a method to derive nonlinear superconformal symmetry in quantum systems via reduction procedures, clarifying the origin of quantum corrections to symmetry generators.

Findings

Reduction produces a superconformal mechanics model with coupled degrees of freedom.

Quantum corrections to integrals of motion are explicitly identified.

The form of the nonlinear superconformal algebra is fully determined.

Abstract

We show that the reduction of a planar free spin-1/2 particle system by the constraint fixing its total angular momentum produces the one-dimensional Akulov-Pashnev-Fubini-Rabinovici superconformal mechanics model with the nontrivially coupled boson and fermion degrees of freedom. The modification of the constraint by including the particle's spin with the relative weight $n\in \N$, $n>1$, and subsequent application of the Dirac reduction procedure (`first quantize and then reduce') give rise to the anomaly free quantum system with the order $n$ nonlinear superconformal symmetry constructed recently in hep-th/0304257. We establish the origin of the quantum corrections to the integrals of motion generating the nonlinear superconformal algebra, and fix completely its form.