Quantum Systems on Linear Groups

TL;DR

This paper explores quantized dynamical systems on linear groups, emphasizing geodetic models with affine invariance, and discusses their potential applications in nuclear and hadronic physics, highlighting differences from traditional models.

Contribution

Introduces new quantized models on linear groups with affine invariance, linking classical and quantum integrable lattices, and suggests applications in nuclear and hadronic dynamics.

Findings

Models show potential in nuclear and hadronic physics.

Distinct from traditional Bohr-Mottelson models.

Connections between classical and quantum integrable lattices.

Abstract

Discussed are quantized dynamical systems on orthogonal and affine groups. The special stress is laid on geodetic systems with affinely-invariant kinetic energy operators. The resulting formulas show that such models may be useful in nuclear and hadronic dynamics. They differ from traditional Bohr-Mottelson models where SL$(n,\mathbb{R})$ is used as a so-called non-invariance group. There is an interesting relationship between classical and quantized integrable lattices.