Branched Hamiltonians for a class of Velocity Dependent Potentials

Hamiltonians that are multivalued functions of momenta are of topical interest since they correspond to the Lagrangians containing higher-degree time derivatives. Incidentally, such classes of branched Hamiltonians lead to certain not too well understood ambiguities in the procedure of quantization. Within this framework, we pick up a model that samples the latter ambiguities and simultaneously turns out to be amenable to a transparent analytic and perturbative treatment.