Spin in Schr\"odinger-quantized Pseudoclassical Systems

TL;DR

This paper explores how spin angular momentum is constructed in pseudoclassical systems with Grassmann variables, revealing a preferred algebraic form that leads to superselection sectors of irreducible spin^c(n) representations upon quantization.

Contribution

It identifies a specific algebraic form of spin generators in pseudoclassical systems that results in irreducible spin^c(n) representations after Schr"odinger quantization.

Findings

Preferred algebraic form yields superselection sectors.

Quantization produces irreducible spin^c(n) representations.

Multiple algebraic forms agree on the constraint surface.

Abstract

We examine the construction of the spin angular momentum in systems with pseudoclassical Grassmann variables. In constrained systems there are many different algebraic forms for the dynamical variables that will all agree on the constraint surface. For the angular momentum, a particular form of the generators is preferred, which yields superselection sectors of irreducible spin^c(n) representations rather than reducible so(n) representations when quantized in the Schr\"odinger realization.