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Classical and quantum q-deformed physical systems
A. Lavagno, A. M. Scarfone, P. Narayana Swamy
abstract: On the basis of the non-commutative q-calculus, we investigate a
q-deformation of the classical Poisson bracket in order to formulate a
generalized q-deformed dynamics in the classical regime. The obtained
q-deformed Poisson bracket appears invariant under the action of the
q-symplectic group of transformations. In this framework we introduce the
q-deformed Hamilton's equations and we derive the evolution equation for some
simple q-deformed mechanical systems governed by a scalar potential dependent
only on the coordinate variable. It appears that the q-deformed Hamiltonian,
which is the generator of the equation of motion, is generally not conserved in
time but, in correspondence, a new constant of motion is generated. Finally, by
following the standard canonical quantization rule, we compare the well known
q-deformed Heisenberg algebra with the algebra generated by the q-deformed
Poisson bracket.
- oai_identifier:
- oai:arXiv.org:quant-ph/0605026
- categories:
- quant-ph cond-mat.other hep-th math.QA
- comments:
- 9 pages, accepted for publication in "The European Physical Journal
C"
- doi:
- 10.1140/epjc/s2006-02557-y
- arxiv_id:
- quant-ph/0605026
- journal_ref:
- Eur.Phys.J.C47:253-261,2006
- created:
- 2006-05-02
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