Higher Derivatives and Canonical Formalism

TL;DR

This paper develops a canonical formalism for higher-derivative theories using Dirac's constrained systems approach, showing it aligns with Ostrogradski's formalism in path integral formulation.

Contribution

It introduces a new canonical formalism for higher-derivative theories based on Dirac's method, unifying it with Ostrogradski's approach in path integral expression.

Findings

Formalism based on Dirac's method is compatible with Ostrogradski's formalism.

Path integral expressions are shared between the two formalisms.

Provides a systematic approach for higher-derivative theories.

Abstract

A canonical formalism for higher-derivative theories is presented on the basis of Dirac's method for constrained systems. It is shown that this formalism shares a path integral expression with Ostrogradski's canonical formalism.