Fock Space Representation of Differential Calculus on the Noncommutative Quantum Space

TL;DR

This paper constructs a Fock space representation for differential calculus on quantum space, analyzes its algebraic structure, and explores implications for quantum statistics and transmutation between bosons and fermions.

Contribution

It introduces a complete Fock space framework for quantum space calculus and examines its impact on quantum statistics and particle transmutation.

Findings

Established a consistent algebraic structure for quantum space calculus

Linked the algebra to canonical fermions and bosons

Discussed the concept of statistical transmutation between particles

Abstract

A complete Fock space representation of the covariant differential calculus on quantum space is constructed. The consistency criteria for the ensuing algebraic structure, mapping to the canonical fermions and bosons and the consequences of the new algebra for the statistics of quanta are analyzed and discussed. The concept of statistical transmutation between bosons and fermions is introduced.