The Difficulty of Symplectic Analysis with Second Class Systems

TL;DR

This paper demonstrates that traditional symplectic analysis struggles with second class constraints and introduces a modified approach to address this issue, improving the method's applicability in constrained systems.

Contribution

The paper identifies limitations of symplectic analysis with second class constraints and proposes a modified method to overcome these challenges.

Findings

Symplectic analysis fails with second class constraints in its original form.

A modified symplectic analysis method successfully handles second class constraints.

The proposed modification enhances the reliability of symplectic analysis in constrained systems.

Abstract

Using the basic concepts of chain by chain method we show that the symplectic analysis, which was claimed to be equivalent to the usual Dirac method, fails when second class constraints are present. We propose a modification in symplectic analysis that solves the problem.