TL;DR
This paper develops a path integral formulation for the quantum mechanical evolution of a q-oscillator using calculus on the quantum plane, respecting quantum group symmetries.
Contribution
It introduces a novel path integral representation for q-oscillators based on invariant calculus on the quantum plane, linking quantum groups with path integral methods.
Findings
Path integral representation for q-oscillator derived
Utilizes calculus invariant under quantum Euclidean group E(2)q
Connects quantum group symmetries with quantum mechanics
Abstract
Using differential and integral calculi on the quantum plane which are invariant with respect to quantum inhomogeneous Euclidean group E(2)q , we construct path integral representation for the quantum mechanical evolution operator kernel of q-oscillator.
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