Dynamics in a Noncommutative Phase Space

Dynamics in a noncommutative phase space is considered. The noncommuting phase space is taken to be invariant under the quantum group GLq,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.