# Branched Hamiltonians for a class of Velocity Dependent Potentials

## TL;DR

This paper explores branched Hamiltonians linked to velocity-dependent potentials, addressing quantization ambiguities through an analytically tractable model that sheds light on higher-derivative Lagrangian systems.

## Contribution

It introduces a specific model of branched Hamiltonians that clarifies quantization ambiguities in higher-derivative systems with velocity dependence.

## Key findings

- Analytic solutions for the model are obtained.
- Perturbative analysis reveals the structure of quantization ambiguities.
- The model provides insights into the quantization of higher-derivative Hamiltonian systems.

## Abstract

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.