# Natural Hamiltonian formulation of composite higher derivative theories

## TL;DR

This paper introduces a novel Hamiltonian formulation for higher derivative theories derived from variable transformations involving time derivatives, offering advantages over traditional Ostrogradsky methods for better quantization and stability.

## Contribution

It develops a natural Hamiltonian framework for composite higher derivative theories that differs from Ostrogradsky's approach, facilitating quantization and stability analysis.

## Key findings

- A new Hamiltonian formulation for higher derivative theories.
- The formulation naturally incorporates constraints and canonical variables.
- Illustrations demonstrate advantages over traditional methods.

## Abstract

If a higher derivative theory arises from a transformation of variables that involves time derivatives, a tailor-made Hamiltonian formulation is shown to exist. The details and advantages of this elegant Hamiltonian formulation, which differs from the usual Ostrogradsky approach to higher derivative theories, are elaborated for mechanical systems and illustrated for simple examples. Both a canonical space and a set of constraints emerge naturally from the transformation rule for the variables. In other words, the setting for quantization and the procedure for eliminating instabilities arise naturally.