A TOPOLOGICAL LAGRANGIAN FOR MONOPOLES ON FOUR-MANIFOLDS

TL;DR

This paper introduces a topological quantum field theory for monopoles on four-manifolds, constructed via the Mathai-Quillen formalism, leading to new topological invariants.

Contribution

It develops a geometrically constructed topological quantum field theory for monopoles, expanding the toolkit for studying four-manifold invariants.

Findings

Defines a new topological quantum field theory for monopoles

Constructs observables that yield new topological quantities

Provides a geometric framework using Mathai-Quillen formalism

Abstract

We present a topological quantum field theory which corresponds to the moduli problem associated to Witten's monopole equations for four-manifolds. The construction of the theory is carried out in purely geometrical terms using the Mathai-Quillen formalism, and the corresponding observables are described. These provide a rich set of new topological quantites.