Higher derivative field theories: degeneracy conditions and classes

Marco Crisostomi, Remko Klein, Diederik Roest

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We provide a full analysis of ghost free higher derivative field theories with coupled degrees of freedom. Assuming the absence of gauge symmetries, we derive the degeneracy conditions in order to evade the Ostrogradsky ghosts, and analyze which (non)trivial classes of solutions this allows for. It is shown explicitly how Lorentz invariance avoids the propagation of "half" degrees of freedom. Moreover, for a large class of theories, we construct the field redefinitions and/or (extended) contact transformations that put the theory in a manifestly first order form. Finally, we identify which class of theories cannot be brought to first order form by such transformations.
Original languageEnglish
Pages (from-to)1-29
Number of pages30
JournalJournal of High Energy Physics
Issue number6
Publication statusPublished - 23 Jun 2017


  • hep-th
  • astro-ph.CO
  • gr-qc
  • classical theories of gravity
  • cosmology of theories beyond the SM


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