Modified Ostrogradski formulation of field theory

TL;DR

This paper introduces a modified Hamiltonian approach for second-derivative field theories, treating all derivatives as independent variables, enhancing the Ostrogradski formalism, with applications to scalar fields and General Relativity.

Contribution

It proposes a novel Hamiltonian formulation that considers all derivatives as independent, improving upon the traditional Ostrogradski method for higher-order field theories.

Findings

Consistent formulation for second order scalar fields.

Application outline for General Relativity.

Demonstrated formalism with simple examples.

Abstract

We present a method for the Hamiltonian formulation of field theories that are based on Lagrangians containing second derivatives. The new feature of our formalism is that all four partial derivatives of the field variables are initially considered as independent fields, in contrast to the conventional Ostrogradski method, where only the velocity is turned into an independent field variable. The consistency of the formalism is demonstrated by simple unconstrained and constrained second order scalar field theories. Its application to General Relativity is briefly outlined.