Clifford algebras, meson algebras and higher order generalisations

TL;DR

This paper explores the structure of Clifford and meson algebras, relating their homogeneous parts to fermionic parastatistics of various orders, and introduces higher order generalizations of these algebras.

Contribution

It extends Clifford and meson algebras to include higher order fermionic parastatistics, providing a new framework for their algebraic structures.

Findings

Clifford algebra relates to fermionic parastatistics of order 1

Meson algebra relates to fermionic parastatistics of order 2

Higher order generalizations of these algebras are constructed

Abstract

We analyse the homogeneous parts of Clifford and meson algebras and point out that for the Clifford algebra it is related to fermionic statistics, that is, to fermionic parastatistics of order 1 while for the meson algebra it is related to fermionic parastatistics of order 2. We extend these homogeneous algebras into corresponding algebras related to fermionic parastatistics of all orders. We then define correspondingly higher order generalizations of Clifford and meson algebras.