Quantum groups, q-dynamics and Rajaji

TL;DR

This paper explores the application of quantum groups to q-deformed harmonic oscillators, maintaining symmetries, and briefly discusses Rajaji's role in mathematical physics.

Contribution

It introduces a framework combining quantum groups with q-deformed oscillators on a quantum line, respecting multiple symmetries.

Findings

Quantum groups can be applied to q-deformed oscillators.

Symmetries like $GL_{qp}(2)$ and rotational invariance are preserved.

The approach offers insights into q-dynamics on quantum lines.

Abstract

We sketch briefly the essentials of the quantum groups and their application to the dynamics of a q-deformed simple harmonic oscillator moving on a quantum line, defined in the q-deformed cotangent (momentum phase) space. In this endeavour, the quantum group $GL_{qp} (2)$- and the conventional rotational invariances are respected together. During the course of this discussion, we touch upon Rajaji's personality as a critical physicist and a bold and adventurous man of mathematical physics.