On the symmetry definitions for the constraint dynamical systems

TL;DR

This paper proposes a symmetry definition for constrained Hamiltonian systems that aligns with the classical non-constrained case, enabling analysis of the entire Hamiltonian spectrum.

Contribution

It introduces a symmetry definition for constraint dynamical systems that unifies the treatment of the full Hamiltonian spectrum, improving upon previous fragmented approaches.

Findings

The new symmetry definition is consistent with classical Hamiltonian symmetries.

It allows analysis of the entire Hamiltonian spectrum without splitting.

The approach simplifies the study of constrained dynamical systems.

Abstract

The problem of proper symmetry definition for constraint dynamical systems with Hamiltonians is considered. Finally, we choose a definition of symmetry which agrees with the analogous definition used for the non-constraint dynamical systems with Hamiltonians. Our symmetry definition allows one to consider the whole spectrum of the Hamiltonian without splitting it into a few different parts.