Higher Derivatives and Canonical Formalisms

TL;DR

This paper derives path integral expressions for three canonical formalisms of higher-derivative theories, showing their equivalence and connections, including the generalized formalism's relation to the constrained one via canonical transformation.

Contribution

It provides unified path integral formulations for Ostrogradski's, constrained, and generalized formalisms, highlighting their equivalence and the canonical transformation linking the generalized and constrained approaches.

Findings

All three formalisms share the same path integral expressions.

The generalized formalism is connected to the constrained one by a canonical transformation.

The formulations apply to both nonsingular and singular cases.

Abstract

Path integral expressions for three canonical formalisms -- Ostrogradski's one, constrained one and generalized one -- of higher-derivative theories are given. For each fomalism we consider both nonsingular and singular cases. It is shown that three formalisms share the same path integral expressions. In paticular it is pointed out that the generalized canonical formalism is connected with the constrained one by a canonical transformation.