A path integral formulation in the representation of coherent states for the quantum group SU q (2) is introduced. An expression for the transition amplitude connecting two SU q (2) coherent states is constructed, and the corresponding canonical equations of motion are also derived.
Path integral in the representation of coherent state for the simplest semisimple Lie group SU(2) and its classical consequences are investigated. Using the completeness relation of the coherent state, we derive a path integral expression for the transition amplitude which connects a pair of SU(2) coherent states. In the classical limit we arrive at a canonical equation of motion in a ’’curved phase space’’ (two-dimensional sphere) which reproduces the ordinary Euler’s equation of a rigid body when applied to a rotator.