Related papers: L^2-Kernels Of Dirac-Type Operators On Monopole Mo…
In this paper, by using the decomposition theorem for weak Hardy spaces, we will obtain the boundedness properties of some integral operators with variable kernels on these spaces, under some Dini type conditions imposed on the variable…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
The Dirac monopole on a three-dimensional torus is considered as a solution to the Bogomolny equation with non-trivial boundary conditions. The analytical continuation of the obtained solution is shown to be a three-dimensional…
Spaces of differential forms over configuration spaces with Poisson measures are constructed. The corresponding Laplacians (of Bochner and de Rham type) on 1-forms and associated semigroups are considered. Their probabilistic interpretation…
The space of m-ary differential operators acting on weighted densities is a (m+1)-parameter family of modules over the Lie algebra of vector fields. For almost all the parameters, we construct a canonical isomorphism between this space and…
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…
We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic estimates for such operators and hence deduce that these…
We present a formula for the Hilbert series that counts gauge invariant chiral operators in a large class of 3d ${\cal N} \ge 2$ Yang-Mills-Chern-Simons theories. The formula counts 't Hooft monopole operators dressed by gauge invariants of…
We consider monopoles with singularities of Dirac type on quasiregular Sasakian three-folds fibering over a compact Riemann surface $\Sigma$, for example the Hopf fibration $S^3\longrightarrow S^2$. We show that these correspond to…
We study the BPS states of the M-fivebrane which correspond to monopoles of N=2 SU(2) gauge theory. Far away from the centres of the monopoles these states may be viewed as solitons in the Seiberg-Witten effective action. It is argued that…
We review classical BPS monopoles, their moduli spaces, twistor descriptions and dynamics. Particular emphasis is placed upon symmetric monopoles, where recent progress has been made. Some remarks on the role of monopoles in S-duality and…
We show that noncommutative electromagnetism and Dirac-Born-Infeld (DBI) theory with scalar fields are SL(2,R) self-dual when noncommutativity is light-like and we are in the slowly varying field approximation. This follows from SL(2,R)…
We construct the hyper-K\"ahler moduli space of framed monopoles over $\mathbb{R}^3$ for any connected, simply connected, compact, semisimple Lie group and arbitrary mass and charge, and hence symmetry breaking. In order to do so, we define…
Let G be a compact connected semisimple Lie group and let H\subset G be a closed connected subgroup such that rank(G)=rank(H) and G/H is a symmetric space. Given an irreducible representation of H, we define a Dirac operator D and determine…
We study magnetic monopoles in a Lorentz- and CPT-odd electrodynamical framework in (3+1) dimensions. This is the standard Maxwell model extended by means of a Chern-Simons-like term, $b_\mu\tilde{F}^{\mu\nu}A_\nu$ ($b_\mu$ constant), which…
By using Meng's idea in his generalization of the classical MICZ-Kepler problem, we obtained the equations of motion of a charged particle in the field of generalized Dirac monopole in odd dimensional Euclidean spaces. The main result is…
We characterize those sequences of weighted isobaric polynomials as defined in math.CO/0106213 which belong to the kernel of the linear operator $D_{11} - \sum_{j=1}^k a_j t_j D_{2j} - mD_2$, and we characterize those linear operators of…
In this paper we are interested in generalizing Keller-type eigenvalue estimates for the non-selfadjoint Schr\"{o}dinger operator to the Dirac operator, imposing some suitable rigidity conditions on the matricial structure of the potential,…
Usually the quantum spin Hall states are expected to possess gapless, helical edge modes. Are there clean, non-interacting, quantum spin Hall states without gapless, edge modes? We show the generic, $n$-fold-symmetric, momentum planes of…
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…