dorsal/arxiv
View SchemaDeformed Heisenberg algebra: origin of q-calculus
| Authors | P. Narayana Swamy |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0305032 |
| URL | https://arxiv.org/abs/quant-ph/0305032 |
Abstract
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.
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"abstract": "The intimate connection between q-deformed Heisenberg uncertainty relation\nand the Jackson derivative based on q-basic numbers has been noted in the\nliterature. The purpose of this work is to establish this connection in a clear\nand self-consistent formulation and to show explicitly how the Jackson\nderivative arises naturally. We utilize a holomorphic representation to arrive\nat the correct algebra to describe q-deformed bosons. We investigate the\nalgebra of q-fermions and point out how different it is from the theory of\nq-bosons. We show that the holomorphic representation for q-fermions is indeed\nfeasible in the framework of the theory of generalized fermions. We also\nexamine several different q-algebras in the context of the modified Heisenberg\nequation of motion.",
"arxiv_id": "quant-ph/0305032",
"authors": [
"P. Narayana Swamy"
],
"categories": [
"quant-ph"
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"title": "Deformed Heisenberg algebra: origin of q-calculus",
"url": "https://arxiv.org/abs/quant-ph/0305032"
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