Exorcising the Ostrogradsky ghost in coupled systems

Remko Klein*, Diederik Roest

*Corresponding author for this work

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The Ostrogradsky theorem implies that higher-derivative terms of a single mechanical variable are either trivial or lead to additional, ghost-like degrees of freedom. In this letter we systematically investigate how the introduction of additional variables can remedy this situation. Employing a Lagrangian analysis, we identify conditions on the La-grangian to ensure the existence of primary and secondary constraints that together imply the absence of Ostrogradsky ghosts. We also show the implications of these conditions for the structure of the equations of motion as well as possible redefinitions of the variables. We discuss applications to analogous higher-derivative field theories such as multi-Galileons and beyond Horndeski.

Original languageEnglish
Article number130
Number of pages16
JournalJournal of High Energy Physics
Issue number7
Publication statusPublished - 27-Jul-2016


  • Classical Theories of Gravity
  • Cosmology of Theories beyond the SM

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