A q-analogue of Nahm's formalism for self-dual gauge fields

TL;DR

This paper introduces a q-analogue of Nahm's formalism for self-dual gauge fields, incorporating a deformation parameter q and utilizing basic hypergeometric series, which recovers the classical monopole solution as q approaches 1.

Contribution

It develops a novel q-deformation of Nahm's formalism for BPS monopoles using hypergeometric series, extending the classical theory.

Findings

The q-analogue reproduces the BPS monopole as q approaches 1.

The formalism employs basic hypergeometric series.

It provides a new mathematical framework for self-dual gauge fields.

Abstract

We present a q-analogue of Nahm's formalism for the BPS monopole, which gives self-dual gauge fields with a deformation parameter q. The theory of the basic hypergeometric series is used in our formalism. In the limit q -> 1 the gauge fields approach the BPS monopole and Nahm's result is reproduced.