Exploring Branched Hamiltonians for a Class of Nonlinear Systems

TL;DR

This paper investigates branched Hamiltonians arising from higher-order derivatives in nonlinear systems, demonstrating feasible quantization methods for specific Lienard-type models.

Contribution

It introduces a novel approach to quantizing nonlinear systems with branched Hamiltonians, addressing ambiguities from higher-order derivatives.

Findings

Two nonlinear models admit feasible quantization.

Branched Hamiltonians can be effectively used in nonlinear system analysis.

Provides insights into quantization ambiguities in higher-derivative systems.

Abstract

One of the less well understood ambiguities of quantization is emphasized to result from the presence of higher-order time derivatives in the Lagrangians resulting in multiple-valued Hamiltonians. We explore certain classes of branched Hamiltonians in the context of nonlinear autonomous differential equation of Lienard type. Two eligible elementary nonlinear models that emerge are shown to admit a feasible quantization along these lines.