A unifying framework for ghost-free Lorentz-invariant Lagrangian field theories
arXiv:1508.03247 · doi:10.1016/j.physletb.2017.06.073
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.
8 pages, two columns, final version
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- Second order differential equations for bosons with spin j > 1 and in the bases of general tensor-spinors of rank-2j