Perturbative Approach to Higher Derivative and Nonlocal Theories

TL;DR

This paper reviews a perturbative method for handling higher and infinite order derivatives in Lagrangians, enabling the construction of consistent Hamiltonian structures and analyzing noncommutative field theories.

Contribution

It introduces a systematic perturbative approach to formulate Hamiltonian dynamics for theories with higher derivatives, including nonlocal and noncommutative models.

Findings

Hamiltonian constructed order by order in coupling

Hamiltonian bounded from below at lowest order

Applicable to spacetime noncommutative field theories

Abstract

We review a perturbative approach to deal with Lagrangians with higher or infinite order time derivatives. It enables us to construct a consistent Poisson structure and Hamiltonian with only first time derivatives order by order in coupling. To the lowest order, the Hamiltonian is bounded from below whenever the potential is. We consider spacetime noncommutative field theory as an example.