Topological quantization of the free massive bosonic field

TL;DR

This paper introduces a topological quantization method for free massive bosonic fields, using geometric and fiber bundle techniques to analyze their topological spectra and energy implications.

Contribution

It presents the first example of classical field quantization via topology, applying harmonic maps and fiber bundles to free massive bosonic fields in two dimensions.

Findings

Topological spectra are characterized by the Euler invariant.

Specific configurations influence the system's energy.

Geometric representation aids in understanding quantum aspects.

Abstract

We present a topological quantization of free massive bosonic fields as the first example of a classical field theory with a quantum counterpart to be studied under this formalism. First, we identify certain harmonic map as a geometric representation of this physical system. We take as a concrete example the case of free massive bosonic fields in two dimensions represented by the minimal embedding of a two dimensional surface into a pp-wave spacetime. We use this geometric representation to construct the fiber bundle corresponding to some specific field configurations and then find their topological spectra, defined in terms of the Euler invariant. We discuss the results for some particular configurations and their consequences for the energy of the system.