Affine symmetry in mechanics of collective and internal modes. Part II. Quantum models

TL;DR

This paper presents a quantum model for affine modes in mechanics, reducing complexity and exploring applications in nuclear physics, including the possibility of half-integer angular momentum in spin-less systems.

Contribution

It introduces a Schrödinger quantization of affine modes, reducing the degrees of freedom and discussing novel quantum effects in many-body systems.

Findings

Effective reduction of degrees of freedom from n^2 to n

Potential for half-integer angular momentum in spin-less particles

Applications suggested for nuclear physics and quantum many-body problems

Abstract

Discussed is the quantized version of the classical description of collective and internal affine modes as developed in Part I. We perform the Schr\"odinger quantization and reduce effectively the quantized problem from $n^{2}$ to $n$ degrees of freedom. Some possible applications in nuclear physics and other quantum many-body problems are suggested. Discussed is also the possibility of half-integer angular momentum in composed systems of spin-less particles.