Related papers: Spherical harmonics and integration in superspace …
We introduce the concept of optical coherence squeezing in double-slit interference. We construct Hermitian operators that characterize the coherence at the slits, leading to coherence uncertainty relations and a corresponding squeezing…
According to Sakellaridis, many zeta integrals in the theory of automorphic forms can be produced or explained by appropriate choices of a Schwartz space of test functions on a spherical homogeneous space, which are in turn dictated by the…
A systematic search for superintegrable quantum Hamiltonians describing the interaction between two particles with spin 0 and 1/2, is performed. We restrict to integrals of motion that are first-order (matrix) polynomials in the components…
A complete classification of locally spherically symmetric four-dimensional Lorentzian spacetimes is given in terms of their local conformal symmetries. The general solution is given in terms of canonical metric types and the associated…
The spherical harmonics $Y_{\ell m}(\theta,\varphi)$ are complex-valued functions on the surface of a sphere, and have found widespread application in physics and astronomy. Every physics students knows them from quantum mechanics and…
In the last decade there has been a growing interest in superoscillations in various fields of mathematics, physics and engineering. However, while in applications as optics the local oscillatory behaviour is the important property, some…
We are interested in the harmonic analysis on $p$-adic homogeneous spaces based on spherical functions. In the present paper, we investigate the space $X$ of unitary hermitian matrices of size $m$ over a ${\mathfrak p}$-adic field $k$ and…
This paper provides a rigorous account on the geometry of forms on supermanifolds, with a focus on its algebraic-geometric aspects. First, we introduce the de Rham complex of differential forms and we compute its cohomology. We then discuss…
In the past decade there has been a flurry of activity at the intersection of spectral theory and symplectic geometry. In this paper we review recent results on semiclassical spectral theory for commuting Berezin-Toeplitz and…
This paper establishes a rigorous geometrical framework for spherical origami, origami using spherical sheets based on spherical geometry. Two settings are treated: origami restricted to the unit sphere ($\mathbb{S}^2$), and…
The symmetry structure of twodimensional nonlinear isotropic oscillator, introduced in Physica D237 (2008) 505, is discussed. It is shown that it possesses three independent integrals of motion which can be chosen in such a way that they…
We give a brief account of two recent applications of the harmonic superspace method: (i) an off-shell description of torsionful $(4,4)$ supersymmetric $2D$ sigma models in the framework of $SU(2)\times SU(2)$ harmonic superspace and (ii)…
Berezin integration over fermionic degrees of freedom as a standard tool of quantum field theory is analysed from the viewpoint of noncommutative geometry. It is shown that among the variety of contradictory integration prescriptions…
This paper is devoted to certain applications of classical Whitney decomposition of the upper half space R^n+1 to various problems in harmonic function spaces in the upper half space.We obtain sharp new assertions on embeddings,distances…
We derive an integral formula for the linking number of two submanifolds of the n-sphere S^n, of the product S^n x R^m, and of other manifolds which appear as "nice" hypersurfaces in Euclidean space. The formulas are geometrically…
We present a conceptual and uniform interpretation of the methods of integral representations of L-functions (period integrals, Rankin-Selberg integrals). This leads to: (i) a way to classify of such integrals, based on the classification…
In this paper, we give an alternative proof of separation of variables for scalar-valued polynomials $P:(\mathbb R^m)^k\to\mathbb C$ in the semistable range $m\geq 2k-1$ for the symmetry given by the orthogonal group $O(m)$. It turns out…
We describe the relationship between complex-valued harmonic morphisms from Minkowski 4-space} and the shear-free ray congruences of mathematical physics. Then we show how a horizontally conformal submersion on a domain of Euclidean 3-space…
We investigate numerical methods for wave equations in $n+2$ spacetime dimensions, written in spherical coordinates, decomposed in spherical harmonics on $S^n$, and finite-differenced in the remaining coordinates $r$ and $t$. Such an…
The main result of this article is that we show that from supersymmetry we can generate new superintegrable Hamiltonians. We consider a particular case with a third order integral and apply the Mielnik's construction in supersymmetric…