Symplectic algorithm for systems with second-class constraints

TL;DR

This paper applies a modified Faddeev-Jackiw symplectic algorithm to systems with second-class constraints, demonstrating its consistency with Dirac's approach in both field theory and mechanical models.

Contribution

It introduces a modified symplectic algorithm tailored for second-class constraints and validates it against established Dirac formalism.

Findings

Constraints match Dirac's canonical results

Algorithm successfully applied to chiral Schwinger model

Applicable to mechanical systems with second-class constraints

Abstract

The recently modified Faddeev-Jackiw formalism for systems having one chain of four levels of only second-class constraints is applied to the non-trivial a=1 bosonized chiral Schwinger model in (1+1) dimensions as well as to one mechanical system. The sets of obtained constraints are in agreement with Dirac's canonical formulation.