Paper detail

Canonical formulation of Pais-Ulhenbeck action and resolving the issue of branched Hamiltonian

Shortcomings of Dirac's constrained analysis in the context of fourth order Pais-Uhlenbeck oscillator action and the appearance of badly affected phase-space Hamiltonian for a generalized fourth order oscillator action, following Ostrogradski, Dirac and Horowitz's formalism, require a viable canonical formulation. This is achieved only after fixing appropriate variables at the end points and taking care of the counter surface terms obtained from variational principle. In the process a one-to-one correspondence between different higher order theories has been established. On the other hand the issue of branched Hamiltonian appearing in the presence of velocities with degree higher than two in the Lagrangian, has not been resolved uniquely as yet. However, often such terms appear with higher order theory, gravity in particular. Here we show that canonical formulation of higher order theory takes care of the issue elegantly.