Ostrogradsky's Hamilton formalism and quantum corrections

TL;DR

This paper compares the Lagrange and Ostrogradsky's Hamilton formalisms in higher-derivative scalar field theories, showing they agree classically but diverge when quantum corrections are considered.

Contribution

It highlights the discrepancy between classical and quantum results in higher-derivative theories using a simple scalar field model.

Findings

Classical equivalence of formalisms confirmed

Quantum corrections cause divergence between approaches

Implications for quantization of higher-derivative theories

Abstract

By means of a simple scalar field theory it is demonstrated that the Lagrange formalism and Ostrogradsky's Hamilton formalism in the presence of higher derivatives, in general, do not lead to the same results. While the two approaches are equivalent at the classical level, differences appear due to the quantum corrections.