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

Understand

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.