arXiv research

Vortex solutions on flat surfaces map to harmonic spinors on Nappi-Witten space.

We propose a new definition for the abelian magnetic charge density of a non-abelian monopole, based on zero-modes of an associated Dirac operator. Unlike the standard definition of the charge density, this density is smooth in the core of the monopole. We show that this charge density induces a magnetic field whose ex…

We develop a method for finding the zero modes of the Dirac operator in the presence of BPS monopoles. We use it to find the zero modes in the case of Abelian BPS monopoles in $\mathbb R^3$.

Paper proves a spinor inequality for magnetic fields on spin manifolds.

There are few known computable examples of non-abelian surface holonomy. In this paper, we give several examples whose structure 2-groups are covering 2-groups and show that the surface holonomies can be computed via a simple formula in terms of paths of 1-dimensional holonomies inspired by earlier work of Chan Hong-Mo…

Study on vortex sheet formation in Abelian gauge theories.

Revisits zero modes of Dirac operator on Eguchi-Hanson space.

The paper analyzes zero modes on product manifolds and provides estimates for their norms.

The paper proves inequalities for zero mode equations on spin manifolds.

Introduces a massive variant of Ray-Singer Torsion to avoid zero modes in topological field theories.

We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism …

Let $(M^\circ, g)$ be an asymptotically conic manifold, in the sense that $M^\circ$ compactifies to a manifold with boundary $M$ in such a way that $g$ becomes a scattering metric on $M$. A special case of particular interest is that of asymptotically Euclidean manifolds, where $\partial M = S^{n-1}$ and the induced me…

This paper studies the space of $L ^2$ harmonic forms and $L ^2$ harmonic spinors on Taub-bolt, a Ricci-flat Riemannian 4-manifold of ALF type. We prove that the space of harmonic square-integrable 2-forms on Taub-bolt is 2-dimensional and construct a basis. We explicitly find a 2-parameter family of $L ^2$ zero mod…

New principle for supersymmetric localization on Lie groups.

We give estimates for the eigenvalues of multi-form modified Dirac operators which are constructed from a standard Dirac operator with the addition of a Clifford algebra element associated to a multi-degree form. In particular such estimates are presented for modified Dirac operators with a $k$-degree form $0\leq k\leq…

Challenge to separate Earth's magnetic field from vehicle's magnetic field for accurate navigation.

Extends E. Hopf's theorem to magnetic systems without conjugate points.

A magnetic field is defined by the property that its divergence is zero in a three dimensional oriented Riemannian manifold. Each magnetic field generates a magnetic flow whose trajectories are curves called as magnetic curves. In this paper, we give a new variational approach to studies the magnetic flow asociated wit…

Compatibility equations adapted to magnetic geometry.

This paper studies Hamilton-Jacobi equations for magnetic systems with constraints.

Magnetic Brunn-Minkowski inequalities on Riemannian manifolds

Study shows finiteness of magnetic hypersurfaces on closed manifolds.

The paper studies magnetic curves in $C$-manifolds and their properties.

New tensors help solve magnetic flow integrability.

Study magnetic geodesics on Heisenberg groups and manifolds.

Paper introduces magnetic Hodge Laplacian for differential forms.

In the paper we prove the existence of the strict but relative relation between small exotic $\mathbb{R}^{4}$ for a fixed radial family of DeMichelis-Freedman type, and cobordism classes of codimension one foliations of $S^{3}$ distinguished by the Godbillon-Vey invariant, $GV\in H^{3}(S^{3},\mathbb{R})$ (represented b…

We explicitly determine all magnetic curves corresponding to the Killing magnetic fields on the 3-dimensional Euclidean space.

Study of magnetic geodesics on Heisenberg nilmanifolds.

Using the submanifold quantum mechanical scheme, the restricted Dirac operator in a submanifold is defined. Then it is shown that the zero mode of the Dirac operator expresses the local properties of the submanifold, such as the Frenet-Serret and generalized Weierstrass relations. In other words this article gives a re…

Study magnetic Steklov eigenvalues on manifolds with boundary.

Study magnetic potentials on Anosov manifolds using spectral data.

Examples are presented of how the geometric notion of the mean curvature is used for general magnetic field configurations and magnetic surfaces. It is shown that the mean magnetic curvature is related to the variation of the absolute value of the magnetic field along its lines. Magnetic surfaces of constant mean curva…

Study magnetic curvature on Lie groups, extending Milnor's work.

In this paper we study rigidity aspects of Zoll magnetic systems on closed surfaces. We characterize magnetic systems on surfaces of positive genus given by constant curvature metrics and constant magnetic functions as the only magnetic systems such that the associated Hamiltonian flow is Zoll, i.e. every orbit is clos…

Study shows magnetic trajectories in Berger spheres are homogeneous.

Extends magnetic flow theory results to higher dimensions.

The paper explores how magnetic systems' spectra can identify metrics and 1-forms.

Study magnetic flows on 3D contact sub-Riemannian manifolds using Rumin complex.

Metrics are isometric for certain Anosov magnetic systems.

Study on magnetic Dirac operators and their spectrum.

In a three-dimensional Riemannian manifold M that admits a unit Killing vector field $ξ$, we regard $ξ$ as a magnetic vector field. A magnetic Hopf surface is a surface obtained by Lie dragging the magnetic curve with $ξ$. Then we characterize Sasakian structure on M from magnetic Hopf surfaces. That is, we show that i…

A quasiclassical method approximates magnetic monopole eigenvalues.

Researchers compute trace formula for magnetic Laplacian on hyperbolic surfaces.

Homogeneous magnetic trajectories in a special linear group proven.

Study on Killing magnetic curves in Heisenberg group geometry.

We interpret magnetic billiards as Finsler ones and describe an analog of the string construction for magnetic billiards. Finsler billiards for which the law "angle of incidence equals angle of reflection" are described. We characterize the Finsler metrics in the plane whose geodesics are circles of a fixed radius. Thi…

Homogeneous magnetic paths found in Heisenberg space.