Dynamics in a noncommutative phase space

Abstract

Dynamics has been generalized to a noncommutative phase space. The noncommuting phase space is taken to be invariant under the quantum group $G{L}_{q,p}(2)$. The $q$-deformed differential calculus on the phase space is formulated and using this, both the Hamiltonian and Lagrangian forms of dynamics have been constructed. In contrast to earlier forms of $q$-dynamics, our formalism has the advantage of preserving the conventional symmetries such as rotational or Lorentz invariance.

LaTeX-twice, 16 pages

References in corpus (8)

• Uncertainty Relation in Quantum Mechanics with Quantum Group Symmetry
• Exactly Solvable Potentials and Quantum Algebras
• Black Hole Statistics
• Quantum Group Gauge Theories and Covariant Quantum Algebras
• Lagrangian formulation of some q-deformed systems
• Quantum Particle on a Quantum Circle
• Non-commutative quantum dynamics
• Fock Space Representation of Differential Calculus on the Noncommutative Quantum Space

Cited by in corpus (5)

• UV divergence-free QFT on noncommutative plane
• Isotropic representation of noncommutative 2D harmonic oscillator
• Hamiltonian and Lagrangian Dynamics in a Noncommutative Space
• Noncommutativity In The Mechanics Of A Free Massless Relativistic Particle
• Cohomological Operators and Covariant Quantum Superalgebras