Physics – Quantum Physics
Scientific paper
2003-05-06
Physics
Quantum Physics
11 pages
Scientific paper
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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