Classical and quantum dynamics of noncanonically coupled oscillators and Lie superalgebras

TL;DR

This paper explores the classical and quantum behavior of noncanonically coupled oscillators through the lens of Lie superalgebras, revealing a hidden superhamiltonian structure that preserves operator relations.

Contribution

It introduces a superhamiltonian framework for noncanonically coupled oscillators, linking their dynamics to Lie superalgebras and demonstrating preservation of operator relations.

Findings

Quantum dynamics admits a hidden superhamiltonian formulation.

Operator relations are preserved during evolution.

Lie superalgebras underpin the oscillator dynamics.

Abstract

The classical and quantum dynamics of noncanonically coupled os- cillators is investigated in its relation to Lie superalgebras. It is shown that the quantum dynamics admits a hidden (super)hamiltonian formulation and, hence, preserves the initial operator relations.