Exorcising the Ostrogradsky ghost in coupled systems

Understand

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 Lagrangian 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.