The equivalence between the Hamiltonian and the Lagrangian formulations for the parametrization invariant theories

TL;DR

This paper demonstrates that for parametrization invariant theories, the treatment of singular Lagrangians as field systems aligns exactly with the canonical Hamiltonian approach, clarifying their equivalence.

Contribution

It establishes the exact equivalence between the field system treatment of singular Lagrangians and the canonical Hamiltonian approach in parametrization invariant theories.

Findings

Singular Lagrangians as field systems agree with the canonical approach.

The equivalence holds specifically for parametrization invariant theories.

Clarifies the relationship between different formulations of constrained systems.

Abstract

The link between the tratment of singular Lagrangians as field systems and the canonical Hamiltonian approach is studied. It is shown that the singular Lagrangians as field systems are always in exact agreement with the canonical approach for the parametrization invariant theories.