Path Integrals for Quantum Algebras and the Classical Limit

TL;DR

This paper develops a coherent states path integral formalism for basic quantum algebras, revealing how classical structures emerge with modified geometries and curvature in the classical limit.

Contribution

It introduces a novel path integral approach for quantum algebras like q-oscillator, SU_q(2), and SU_q(1,1), and analyzes their classical limits.

Findings

Classical limit yields modified symplectic and Riemannian structures.

Deformation induces curvature in phase space.

Explicit form of classical structures from quantum algebras.

Abstract

Coherent states path integral formalism for the simplest quantum algebras, q-oscillator, SU_q(2) and SU_q(1,1) is introduced. In the classical limit canonical structure is derived with modified symplectic and Riemannian metric. Non-constant deformation induced curvature for the phase spaces is obtained.