Is it possible to assign physical meaning to field theory with higher derivatives?

TL;DR

This paper proposes a mechanical analogy approach to assign a positive-definite energy to higher-derivative field theories, addressing issues of energy indefiniteness and unitarity violations.

Contribution

It introduces a novel method using the Timoshenko beam theory analogy to define a positive energy in higher-derivative field models, avoiding ghost states.

Findings

Mechanical analogy yields positive definite energy in higher-derivative models

Approach applicable to models with localized solutions like vortices

Addresses unitarity issues in higher-derivative field theories

Abstract

To overcome the difficulties with the energy indefiniteness in field theories with higher derivatives, it is supposed to use the mechanical analogy, the Timoshenko theory of the transverse flexural vibrations of beams or rods well known in mechanical engineering. It enables one to introduce the notion of a "mechanical" energy in such field models that is wittingly positive definite. This approach can be applied at least to the higher derivative models which effectively describe the extended localized solutions in usual first order field theories (vortex solutions in Higgs models and so on). Any problems with a negative norm ghost states and unitarity violation do not arise here.