Related papers: Dirac monopoles from the Matsumoto non-commutative…
Magnetic monopoles have eluded experimental detection since their prediction nearly a century ago by Dirac. Recently it has been shown that classical analogues of these enigmatic particles occur as excitations out of the topological ground…
We shall give a twisted Dirac structure on the space of irreducible connections on a SU(n)-bundle over a three-manifold, and give a family of twisted Dirac structures on the space of irreducible connections on the trivial SU(n)-bundle over…
The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields…
Every $\mathbb{A}^{1}-$bundle over the complex affine plane punctured at the origin, is trivial in the differentiable category but there are infinitely many distinct isomorphy classes of algebraic bundles. Isomorphy types of total spaces of…
We present a recent work on the Dirac equation in a curved spacetime. In addition to the standard equation, two alternative versions are considered, derived from wave mechanics, and based on the tensor representation of the Dirac field. The…
Topology in general but also topological objects such as monopoles are a central concept in physics. They are prime examples for the intriguing physics of gauge theories and topological states of matter. Vector monopoles are already…
Stimulated by a scholium in Newton's Principia we find some beautiful results in classical mechanics which can be interpreted in terms of the orbits in the field of a mass endowed with a gravomagnetic monopole. All the orbits lie on cones!…
A gauge transformation provided by the three eigenfunctions of $\B^a(x) \cdot \B^b(x)$ (where $\B^a(x)$, with a=1,2,3, are the non-Abelian magnetic fields) exposes the topological configurations of the Yang-Mills fields. In particular, it…
A non-abelian topological quantum field theory describing the scattering of self-dual field configurations over topologically non-trivial Riemann surfaces, arising from the reduction of 4-dim self-dual Yang-Mills fields, is introduced. It…
The effective Hamiltonians for chiral supersymmetric gauge theories at small spatial volume are generalizations of the Hamiltonians describing the motion of a scalar or a spinor particle in a field of Dirac monopoles (we are dealing in fact…
Using the Dirac string formalism for monopoles we expose an extensive analogy between magnetic monopole excitations in the dumbbell model of spin ice and those of the vacuum. In both cases the Dirac strings are defined in the space-time of…
The interplay of symmetry and topology has been at the forefront of recent progress in quantum matter. Here we uncover an unexpected connection between band topology and the description of competing orders in a quantum magnet. Specifically…
In this work we examine generalized Connes-Lott models on the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure…
Topological magnons are emergent quantum spin excitations featured by magnon bands crossing linearly at the points dubbed nodes, analogous to fermions in topological electronic systems. Experimental realization of topological magnons in…
We consider twelve different ways of modelling the 3-body problem in dimension $\geq 2$. These can be viewed as models of classical and quantum background independence. We show that a different type of monopole is realized in each's…
A wide class of noncommutative spaces, including 4-spheres based on all the quantum 2-spheres and suspensions of matrix quantum groups is described. For each such space a noncommutative vector bundle is constructed. This generalises and…
We describe the internal composition of a topologically stable monopole carrying a magnetic charge of $6\pi/e$ that arises from the spontaneous breaking of the trinification symmetry $SU(3)_c\times SU(3)_L\times SU(3)_R$ ($G$). Since this…
The non-relativistic dynamics of a spin-1/2 particle in a monopole field possesses a rich supersymmetry structure. One supersymmetry, uncovered by d'Hoker and Vinet, is of the standard type: it squares to the Hamiltonian. In this paper we…
The magnetic monopole was postulated in 1931 by Dirac to explain electric charge quantisation. Searches for pair-produced monopoles are performed at accelerator facilities whenever a new energy regime is made available. In addition,…
A self-contained study of monopole configurations of pure Yang-Mills theories and a discussion of their charges is carried out in the language of principal bundles. A n-dimensional monopole over the sphere S^n is a particular type of…