Interpretation and Extension of the Green's Ansatz for Paraparticles

TL;DR

This paper analyzes Green's ansatz for paraparticles, showing how their commutation relations derive from algebraic structures and proposing a generalized construction for paraparticles of combined orders.

Contribution

It provides a mathematical interpretation of Green's ansatz and introduces a generalized framework for constructing paraparticles of higher order from lower-order constituents.

Findings

Derivation of commutation relations from algebraic comultiplication

Generalization of Green's ansatz for combined paraparticle orders

Construction method for paraparticles of order p from lower orders

Abstract

The anomalous bilinear commutation relations satisfied by the components of the Green's ansatz for paraparticles are shown to derive from the comultiplication of the paraboson or parafermion algebra. The same provides a generalization of the ansatz, wherein paraparticles of order $p=\sum_{\alpha=1}^r p_{\alpha}$ are constructed from r paraparticles of order $p_{\alpha}$, $\alpha$=1,2, ...,r.