The Non-Compact Weyl Equation

TL;DR

This paper introduces a non-compact Weyl equation using infinite-dimensional representations, solves it with Kummer functions, and explores its application in constructing non-compact BPS monopoles via the ADHMN approach.

Contribution

It presents a novel non-compact Weyl equation based on infinite-dimensional sl_2 representations and connects it to monopole construction methods.

Findings

Solutions expressed in terms of Kummer functions

Extension of the ADHMN approach to non-compact monopoles

New framework for non-compact Weyl equations

Abstract

A non-compact version of the Weyl equation is proposed, based on the infinite dimensional spin zero representation of the sl_2 algebra. Solutions of the aforementioned equation are obtained in terms of the Kummer functions. In this context, we discuss the ADHMN approach in order to construct the corresponding non-compact BPS monopoles.