http://arxiv.org/abs/1711.08125
As the first step to extend our understanding of higher-derivative theories, within the framework of analytic mechanics of interacting particles, we construct a ghost-free theory involving third-order time derivative in Lagrangian. We clarify that there is a crucial difference in construction from up-to-second-order-derivative theories. While eliminating linear momentum terms in the Hamiltonian is necessary and sufficient to kill the ghosts associated with the higher derivatives for the Lagrangian with up to second-order derivatives, this is necessary but not sufficient for the Lagrangian with higher than second-order derivatives. We demonstrate that even after eliminating the linear momentum terms ghosts are still lurking and they need to be removed appropriately to make Lagrangian free from the ghosts. 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.
H. Motohashi, T. Suyama and M. Yamaguchi
Thu, 23 Nov 17
32/52
Comments: 5 pages