Lagrangian approach to a symplectic formalism for singular systems

TL;DR

This paper introduces a Lagrangian-based symplectic framework for singular systems, providing a unified approach that overcomes limitations of traditional Hamiltonian methods and enables consistent quantization.

Contribution

It develops a novel Lagrangian approach to construct symplectic structures for singular systems, expanding the applicability of symplectic formalism beyond canonical Hamiltonian systems.

Findings

Unified framework for singular systems

Overcomes limitations of Dirac-Bergmann formalism

Enables algebraically consistent quantization

Abstract

We develop a Lagrangian approach for constructing a symplectic structure for singular systems. It gives a simple and unified framework for understanding the origin of the pathologies that appear in the Dirac-Bergmann formalism, and offers a more general approach for a symplectic formalism, even when there is no Hamiltonian in a canonical sense. We can thus overcome the usual limitations of the canonical quantization, and perform an algebraically consistent quantization for a more general set of Lagrangian systems.