Deformed Heisenberg algebra: origin of q-calculus

P.Narayana Swamy

Physica A: Statistical Mechanics and its Applications, 2003, vol. 328, issue 1, 145-153

Abstract: The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative (JD) based on q-basic numbers has been noted in the literature. The purpose of this work is to establish this connection in a clear and self-consistent formulation and to show explicitly how the JD arises naturally. We utilize a holomorphic representation to arrive at the correct algebra to describe q-deformed bosons. We investigate the algebra of q-fermions and point out how different it is from the theory of q-bosons. We show that the holomorphic representation for q-fermions is indeed feasible in the framework of the theory of generalized fermions. We also examine several different q-algebras in the context of the modified Heisenberg equation of motion.

Keywords: q-calculus; Jackson derivative; Deformed Heisenberg algebra; q-algebra; q-bosons; q-fermions (search for similar items in EconPapers)
Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:328:y:2003:i:1:p:145-153

DOI: 10.1016/S0378-4371(03)00518-1

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