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Fock Space Representation Of Differential Calculus On The Noncommutative Quantum Space

Amrit Kumar Mishra, G. Rajasekaran

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.

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Key concepts: Fock space, Noncommutative geometry, Differential calculus, Fermion, Covariant transformation, Quantum differential calculus, Boson, Mathematics