A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories

TL;DR

This paper introduces a unifying framework for Lorentz-invariant Lagrangian field theories that naturally avoids Ostrogradsky ghosts, using differential forms and generalized Kronecker delta, applicable to various spins including novel spin-2 interactions.

Contribution

It provides a new, general formulation for ghost-free Lorentz-invariant theories, including novel nonlinear derivative terms for spin-2 fields, unifying existing theories and extending to new interactions.

Findings

Framework successfully reformulates known theories for different spins.

Novel nonlinear derivative terms for spin-2 fields introduced.

Ostrogradsky ghosts are absent in the proposed fully nonlinear theories.

Abstract

We propose a framework for Lorentz-invariant Lagrangian field theories where Ostrogradsky's scalar ghosts could be absent. A key ingredient is the generalized Kronecker delta. The general Lagrangians are reformulated in the language of differential forms. The absence of higher order equations of motion for the scalar modes stems from the basic fact that every exact form is closed. The well-established Lagrangian theories for spin-0, spin-1, p-form, spin-2 fields have natural formulations in this framework. We also propose novel building blocks for Lagrangian field theories. Some of them are novel nonlinear derivative terms for spin-2 fields. It is nontrivial that Ostrogradsky's scalar ghosts are absent in these fully nonlinear theories.