Related papers: Monopole harmonics on $\mathbb{CP}^{n-1}$
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
Seiberg-like dualities in $2+1$d quiver gauge theories with $4$ supercharges are investigated. We consider quivers made of various combinations of classical gauge groups $U(N)$, $Sp(N)$, $SO(N)$ and $SU(N)$. Our main focus is the mapping of…
The most general Dirac Hamiltonians in $(1+1)$ dimensions are revisited under the requirement to exhibit a supersymmetric structure. It is found that supersymmetry allows either for a scalar or a pseudo-scalar potential. Their spectral…
We quantize the electromagnetic field in the presence of a static magnetic monopole, within the loop-representation formalism. We find that the loop-dependent wave functional becomes multivalued, in the sense that it acquires a dependence…
The role of supercharge operators is studied in the case of a Dirac particle moving in a constant chromomagnetic field. The Hamiltonian is factorised and the ground state wave function in the case of unbroken supersymmetry is determined.
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…
We introduce N=1 supersymmetric generalization of the mechanical system describing a particle with fractional spin in D=1+2 dimensions and being classically equivalent to the formulation based on the Dirac monopole two-form. The model…
Complex potentials are constructed as Darboux-deformations of short range, radial nonsingular potentials. They behave as optical devices which both refracts and absorbs light waves. The deformation preserves the initial spectrum of energies…
We discuss a set of novel discrete symmetry transformations of the N = 4 supersymmetric quantum mechanical model of a charged particle moving on a sphere in the background of Dirac magnetic monopole. The usual five continuous symmetries…
Classical Maxwell and Maxwell-Chern-Simons (MCS) Electrodynamics in (2+1)D are studied in some details. General expressions for the potential and fields are obtained for both models, and some particular cases are explicitly solved.…
The eigenfunctions and eigenenergies for a Dirac Hamiltonian with equal scalar and vector harmonic oscillator potentials are derived. Equal scalar and vector potentials may be applicable to the spectrum of an antinucleion imbedded in a…
Motivated by recent studies of superconformal mechanics extended by spin degrees of freedom, we construct minimally superintegrable models of spinning particles on 2-sphere, the spin degrees of freedom of which are represented by a 3-vector…
The spectral problem of three-dimensional manifolds M_A admitting Sol-geometry in Thurston's sense is investigated. Topologically M_A are torus bundles over a circle with a unimodular hyperbolic gluing map A. The eigenfunctions of the…
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…
Recently Jarvis has proved a correspondence between SU(N) monopoles and rational maps of the Riemann sphere into flag manifolds. Furthermore, he has outlined a construction to obtain the monopole fields from the rational map. In this paper…
We construct a new N=4 supersymmetric mechanics describing the motion of a particle over a $CP^n$ manifold in U(n) background gauge fields.
Monopole operators play a central role in 3 dimensional supersymmetric dualities: a careful understanding of their spectrum is necessary to match chiral operators on either sides of a conjectured duality. In Chern-Simons theories…
It is well-known that coordinates of a charged particle in a monopole background become noncommutative. In this paper, we study the motion of a charged particle moving on a supersphere in the presence of a supermonopole. We construct a…
We consider quantum models corresponding to superymmetrizations of the two-dimensional harmonic oscillator based on worldline $d=1$ realizations of the supergroup SU$(\,{\cal N}/2\,|1)$, where the number of supersymmetries ${\cal N}$ is…
In this paper we study Clifford and harmonic analysis on some conformal flat spin manifolds. In particular we treat manifolds that can be parametrized by $U / \Gamma$ where $U$ is a simply connected subdomain of either $S^{n}$ or $R^{n}$…