Finite W Algebras and Intermediate Statistics

TL;DR

This paper introduces new realizations of finite W algebras by relaxing constraints and connects them to intermediate statistics, suggesting a framework for generalizing anyon statistics in quantum systems.

Contribution

It constructs novel realizations of finite W algebras and links them to Heisenberg quantization, proposing a potential extension of anyon statistics.

Findings

Finite W algebras are realized through relaxed constraints.

W algebras are connected to Heisenberg quantization for two-particle systems.

The framework suggests a generalization of anyon statistics.

Abstract

New realizations of finite W algebras are constructed by relaxing the usual constraint conditions. Then, finite W algebras are recognized in the Heisenberg quantization recently proposed by Leinaas and Myrheim, for a system of two identical particles in d dimensions. As the anyonic parameter is directly associated to the W-algebra involved in the d=1 case, it is natural to consider that the W-algebra framework is well-adapted for a possible generalization of the anyon statistics.