On the Quantisation of Complex Higher Derivative Theories and Avoiding the Ostrogradsky Ghost

Understand

Generic higher derivative theories are believed to be fundamentally unphysical because they contain Ostrogradsky ghosts.

• We show that within complex classical mechanics it is possible to construct higher derivative theories that circumvent the Ostrogradsky theorem and have a real energy spectrum that is bounded from below.
• The complex theory can be canonically quantised.
• The resulting quantum theory does not suffer from the kinetic instability and maintains the usual probabilistic interpretation without violating the correspondence principle.