Ghost-free theory with third-order time derivatives

Understand

As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of point particles, we construct a ghost-free theory involving third-order time derivatives in Lagrangian.

• While eliminating linear momentum terms in the Hamiltonian is necessary and sufficient to kill the ghosts associated with higher derivatives for Lagrangian with at most second-order derivatives, we find that this is necessary but not sufficient for the Lagrangian with higher than second-order derivatives.
• We clarify a set of ghost-free conditions under which we show that the Hamiltonian is bounded, and that equations of motion are reducible into a second-order system.