Second Class Constraints in a Higher-Order Lagrangian Formalism

TL;DR

This paper explores the formulation of second-class constraints within a higher-order Lagrangian path integral framework, introducing an $Sp(2)$ symmetric approach using conjugate higher-order operators.

Contribution

It proposes a novel Lagrangian path integral with $Sp(2)$ symmetry for systems with second-class constraints, based on conjugate higher-order $ riangle$-operators.

Findings

Developed a new $Sp(2)$ symmetric path integral formulation.

Extended the description of second-class constraints in higher-order systems.

Provided a systematic approach for systems with second-class constraints in Lagrangian formalism.

Abstract

We consider the description of second-class constraints in a Lagrangian path integral associated with a higher-order $\Delta$-operator. Based on two conjugate higher-order $\Delta$-operators, we also propose a Lagrangian path integral with $Sp(2)$ symmetry, and describe the corresponding system in the presence of second-class constraints.