Representations and Properties of Generalized $A_r$ Statistics

TL;DR

This paper introduces a generalized form of $A_r$ quantum statistics, defining its algebraic structure and providing explicit Fock-Hilbert and Bargmann-Fock representations for it.

Contribution

It proposes a new generalization of $A_r$ statistics with a complete algebraic formulation and explicit representation constructions.

Findings

Defined the algebraic relations for generalized $A_r$ statistics

Derived Fock-Hilbert representations

Constructed Bargmann-Fock realizations

Abstract

A generalization of $A_r$ statistics is proposed and developed. The generalized $A_r$ quantum statistics is completely specified by a set of Jacobson generators satisfying a set of triple algebraic relations. Fock-Hilbert representations and Bargmann-Fock realizations are derived.