Classical and quantum q-deformed physical systems
arXiv:quant-ph/0605026 · doi:10.1140/epjc/s2006-02557-y
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.
9 pages, accepted for publication in "The European Physical Journal C"
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- Interacting particles system revisited in the framework of the q-deformed algebra
- Nonextensive statistical effects and strangeness production in hot and dense nuclear matter
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- Enhancement of nonclassical properties of two qubits via deformed operators
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- Nonlinear statistical effects in relativistic mean field theory
- Behavior of a Free Quantum Particle in the Poincaré Upper Half-Plane Geometry
- A Dynamical System with Q-deformed Phase Space Represented in Ordinary Variable Spaces