Quantization of affine bodies. Theory and applications in mechanics of structured media

TL;DR

This paper develops a quantum mechanical framework for affine bodies, exploring their dynamics and potential applications in structured media, nanophysics, and molecular physics, through Hamiltonian formalism and quantization methods.

Contribution

It introduces a quantum approach to affine body dynamics, emphasizing affine invariance and proposing methods for analytical solutions and applications.

Findings

Quantization of affine bodies using Hamiltonian formalism

Development of partial separation of variables techniques

Discussion of applications in structured media and nanophysics

Abstract

Discussed is kinematics and dynamics of bodies with affine degrees of freedom, i.e., homogeneously deformable "gyroscopes". The special stress is laid on the status and physical justification of affine dynamical invariance. On the basis of classical Hamiltonian formalism the Schroedinger quantization procedure is performed. Some methods of the partial separation of variables, analytical treatment and search of rigorous solutions are developed. The possiblity of applications in theory of structured media, nanophysics, and molecular physics is discussed.