Quantization of Nonstandard Hamiltonian Systems

TL;DR

This paper explores the geometric quantization of classical systems with multiple Hamiltonian descriptions, demonstrating how quantum geometry constrains nonstandard quantum theories using a spin-1/2 example.

Contribution

It introduces a geometric framework for quantizing nonstandard Hamiltonian systems and shows how quantum geometry restricts possible quantum theories.

Findings

Quantum geometry imposes restrictions on nonstandard quantum theories

The spin-1/2 system exemplifies the quantization process with multiple Hamiltonians

Geometric quantization can be applied to systems with nonstandard Hamiltonian structures

Abstract

The quantization of classical theories that admit more than one Hamiltonian description is considered. This is done from a geometrical viewpoint, both at the quantization level (geometric quantization) and at the level of the dynamics of the quantum theory. A spin-1/2 system is taken as an example in which all the steps can be completed. It is shown that the geometry of the quantum theory imposes restrictions on the physically allowed nonstandard quantum theories.