Perturbative Hamiltonian constraints for higher order theories

TL;DR

This paper introduces a perturbative Hamiltonian formalism for higher order theories, extending Dirac's method, and validates it through classical and quantum comparisons with exact solutions.

Contribution

It develops a consistent low energy canonical formalism for higher order theories by extending Dirac's method with perturbative constraints.

Findings

Formalism successfully applied to Pais-Uhlenbeck oscillator and scalar field

Classical and quantum results match direct perturbative approaches

Validates the soundness of the proposed formalism

Abstract

We present a method for constructing a consistent low energy canonical formalism for higher order time-derivative theories, extending the Dirac method to include perturbative Hamiltonian constraints. We apply it to two paradigmatic examples: the Pais-Uhlenbeck oscillator and the Bernard-Duncan scalar field. We also compare the results, both at the classical and quantum level, with the ones corresponding to a direct perturbative construction applied to the exact higher order theory. This comparison highligths the soundness of the present formalism.