Related papers: A Mathematical Comment on Lanczos Potential Theory
The primary objective of this paper is to derive explicit formulas for rank one and rank two Drinfeld modules over a specific domain denoted by A. This domain corresponds to the projective line associated with an infinite place of degree…
Discrete quantum groups were introduced as duals of compact quantum groups by Podle\'s and Woronowicz in 1990. Shortly after, they were defined and studied intrinsically by Effros and Ruan, and by this author. In 1998, with the introduction…
By introducing a doublet of electromagnetic four dimensional vector potentials, we set up a manifestly Lorentz covariant and SO(2) duality invariant classical field theory of electric and magnetic charges. In our formulation one does not…
Over the $(1,n)$-dimensional real supercircle, we consider the $\mathcal{K}(n)$-modules of linear differential operators, $\frak{D}^n_{\lambda,\mu}$, acting on the superspaces of weighted densities, where $\mathcal{K}(n)$ is the Lie…
The surface charges associated with $p$-form gauge fields in the Bondi patch of $D$-dimensional Minkowski spacetime are computed. We show that, under the Hodge duality between the field strengths of the dual formulations, electric-like…
We revisit the renormalization group (RG) theoretical perturbation theory on oscillator-type second-order ordinary differential equations. For a class of potentials, we show a simple functional relation among secular coefficients of the…
This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…
We present a detailed study of the scattering system given by the Neumann Laplacian on the discrete half-space perturbed by a periodic potential at the boundary. We derive asymptotic resolvent expansions at thresholds and eigenvalues, we…
Let $D\subset R^d$ be a bounded domain and let \[ L=\frac12\nabla\cdot a\nabla +b\cdot\nabla \] %\[ %L=\frac12\sum_{i,j=1}^da_{i,j}\frac{\partial^2}{\partial x_i\partial x_j}+\sum_{i=1}^db_i\frac{\partial}{\partial x_i}, %\] be a second…
We extend the estimates proved by Donnelly and Fefferman and by Lebeau and Robbiano for sums of eigenfunctions of the Laplacian (on a compact manifold) to estimates for sums of eigenfunctions of any positive and elliptic pseudo-differential…
The geometric Langlands program can be described in a natural way by compactifying on a Riemann surface C a twisted version of N=4 super Yang-Mills theory in four dimensions. The key ingredients are electric-magnetic duality of gauge…
Let $A$ be a finite-dimensional, commutative algebra over $\mathbb{R}$ or $\mathbb{C}$. The notion of $A$-differentiable functions on $A$ is extended to the notion of $A$-differentiable functions on a finitely generated $A$-module $B$. Let…
In this work, we study Lagrangian formulations for self-dual gauge theories, also known as chiral $n$-form gauge theories, for $n = 2p$ in $D = 4p+2$ dimensional spacetime. Motivated by a recent formulation of M5-branes derived from the BLG…
We study the extended prepotentials for the S-duality class of quiver gauge theories, considering them as quasiclassical tau-functions, depending on gauge theory condensates and bare couplings. The residue formulas for the third derivatives…
This thesis is divided in two parts. The first part contains the study of some properties of the electromagnetic duality in 4 dimensions. An extended double potential formalism for linearized gravity is introduced which allows to write an…
We develop the Dirac-Schwinger-Zwanziger (DSZ) quantization of classical abelian gauge theories with general duality structure on oriented Lorentzian four-manifolds $(M,g)$ of arbitrary topology, obtaining, as a result, the…
We demonstrate the role of Drinfeld's quantum double D(G) as a spontaneously broken hidden symmetry in a large class of massive quantum field theories in 1+1 dimensions with compact symmetry group G. Our considerations are independent of…
In this paper we study in detail algebraic properties of the algebra $\mathcal D(W)$ of differential operators associated to a matrix weight of Gegenbauer type. We prove that two second order operators generate the algebra, indeed $\mathcal…
The goal and the main result of the paper is to provide a complete description of the field of rational differential invariants of one class of second order ordinary differential equations with scalar control parameter with respect to Lie…
Quantum field theory on the noncommutative two-dimensional Minkowski space with Grosse-Wulkenhaar potential is discussed in two ways: In terms of a continuous set of generalised eigenfunctions of the wave operator, and directly in position…