2003/05/06 by P. Narayana Swamy, Swamy, P. Narayana
Computer Science · Physics and Astronomy · #Data Visualization and Analytics #FOS: Physical sciences #Nonlinear Waves and Solitons #Quantum Physics (quant-ph) #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0305032
11 pages
arxiv created 2003/05/06 · openalex publication_date 2003/05/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The intimate connection between q-deformed Heisenberg uncertainty relation and the Jackson derivative 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 Jackson derivative 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.