The Canonical Symmetry and Hamiltonian Formalism. II. Hamiltonian Operators

TL;DR

This paper explores how canonical symmetry can be utilized to identify a hierarchy of Hamiltonian operators in a system, emphasizing the importance of invariance conditions in solving the problem.

Contribution

It introduces a method leveraging canonical symmetry and invariance conditions to determine Hamiltonian operator hierarchies, advancing the theoretical framework.

Findings

Canonical symmetry aids in constructing Hamiltonian hierarchies.

Invariance condition is essential for solving the hierarchy problem.

Provides a systematic approach to identify Hamiltonian operators.

Abstract

It is shown how the canonical symmetry is used to look for the hierarchy of the Hamiltonian operators relevant to the system under consideration. It appears that only the invariance condition can be used to solve the problem.