Related papers: The Dirac Monopole and Differential Characters
These lecture notes are a friendly introduction to monopole Floer homology. We discuss the relevant differential geometry and Morse theory involved in the definition. After developing the relation with the four-dimensional theory, our…
We describe equivariant differential characters (classifying equivariant circle bundles with connections), their prequantization, and reduction.
We construct the deformed Dirac monopole on the quantum sphere for arbitrary charge using two different methods and show that it is a quantum principal bundle in the sense of Brzezinski and Majid. We also give a connection and calculate the…
We extend Massey products from cohomology to differential cohomology via stacks, organizing and generalizing existing constructions in Deligne cohomology. We study the properties and show how they are related to more classical Massey…
Artificial monopoles have been engineered in various systems, yet there has been no systematic study of the singular vector potentials associated with the monopole field. We show that the Dirac string, the line singularity of the vector…
Given a smooth proper morphism $f\colon X\rightarrow S$, we introduce a certain derived category where morphisms are permitted to be $\mathcal{O}_S$-linear differential operators. We then prove a generalisation of Serre duality that applies…
We study perturbed Dirac operators of the form $ D_s= D + s\A :\Gamma(E^0)\rightarrow \Gamma(E^1)$ over a compact Riemannian manifold $(X, g)$ with symbol $c$ and special bundle maps $\A : E^0\rightarrow E^1$ for $s>>0$. Under a simple…
We review definitions of generalized parallel transports in terms of Cheeger-Simons differential characters. Integration formulae are given in terms of Deligne-Beilinson cohomology classes. These representations of parallel transport can be…
The supersymmetric analysis of spinning cosmic string spacetime, involving an electron in magnetic fields, has been conducted. We examined the Dirac system within extended special functions known as exceptional orthogonal polynomials.…
The full ``classical" Dirac-Maxwell equations are considered under various simplifying assumptions. A reduction of the equations is performed in the case when the Dirac field is {\em static} and a further reduction is performed in the case…
We use the Nahm transform to construct explicit $L^2$ solutions to the Dirac equation in $\mathbb{R}^3$ in the background of one nonabelian $U(2)$ monopole with one positive and one negative Dirac singularity.
We introduce the notion of extension of 1-motives. Using the dictionary between strictly commutative Picard stacks and complexes of abelian sheaves concentrated in degrees -1 and 0, we check that an extension of 1-motives induces an…
We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is…
The technique of differential intertwining operators (or Darboux transformation operators) is systematically applied to the one-dimensional Dirac equation. The following aspects are investigated: factorization of a polynomial of Dirac…
We analyse in detail the language of partially non-abelian Deligne cohomology and of twisted differential K-theory, in order to describe the geometry of type II superstring backgrounds with D-branes. This description will also provide the…
A description of the properties of \L with complex characters is given. By using these, together with the more familiar \L with real characters, it is shown how certain two dimensional lattice sums, which previously could not be put into…
We derive a cohomological formula for the analytic index of the Dirac-Ramond operator and we exhibit its modular properties.
We introduce and study a family of functions we call the "mock characters". These functions satisfy a number of interesting properties, and of all completely multiplicative arithmetic functions seem to come as close as possible to being…
We introduce a special class of multiple Dirichlet series whose terms are supported on a variety and which admit an Euler product structure. We proposed several conjectures on the analytic properties of these series.
We present a "primitive" way of realizing finite-mass Dirac monopoles in $U(1)$ gauge theories involving a single non-minimally interacting scalar field. Typically, the energy density of this type of monopole is not concentrated at its…