相关论文: The Fischer decomposition for Hodge-de Rham system…
Recently the Fischer decomposition for the H-action of the Pin group on Clifford algebra valued polynomials has been obtained. We apply this tool to get various decompositions of special monogenic and inframonogenic polynomials in terms of…
It is well-known that polynomials decompose into spherical harmonics. This result is called separation of variables or the Fischer decomposition. In the paper we prove the Fischer decomposition for spinor valued polynomials in $k$ vector…
Let D denote the Dirac operator in the Euclidean space R^m. In this paper, we present a refinement of the biharmonic functions and at the same time an extension of the monogenic functions by considering the equation DfD=0. The solutions of…
Spaces of spinor-valued homogeneous polynomials, and in particular spaces of spinor-valued spherical harmonics, are decomposed in terms of irreducible representations of the symplectic group Sp$( p)$. These Fischer decompositions involve…
We establish the basis of a discrete function theory starting with a Fischer decomposition for difference Dirac operators. Discrete versions of homogeneous polynomials, Euler and Gamma operators are obtained. As a consequence we obtain a…
In the framework of quaternionic Clifford analysis in Euclidean space $\mathbb{R}^{4p}$, which constitutes a refinement of Euclidean and Hermitian Clifford analysis, the Fischer decomposition of the space of complex valued polynomials is…
Recently, the Fischer decomposition for polynomials on superspace R^{m|2n} (that is, polynomials in m commuting and 2n anti-commuting variables) has been obtained unless the superdimension M=m-2n is even and non-positive. In this case, it…
Spherical monogenics can be regarded as a basic tool for the study of harmonic analysis of the Dirac operator in Euclidean space R^m. They play a similar role as spherical harmonics do in case of harmonic analysis of the Laplace operator on…
Recently, it has been established that the discrete star Laplace and the discrete Dirac operator, i.e. the discrete versions of their continuous counterparts when working on the standard grid, are rotation-invariant. This was done starting…
We continue the study initiated by H. S. Shapiro on Fischer decompositions of entire functions, showing that such decomposition exist in a weak sense (we do not prove uniqueness) under hypotheses regarding the order of the entire function…
We give a method of decomposing bundle-valued polynomials compatible with the action of the Lie group $Spin(n)$, where important tools are $Spin(n)$-equivariant operators and their spectral decompositions. In particular, the top irreducible…
In this paper we work in the `split' discrete Clifford analysis setting, i.e. the m-dimensional function theory concerning null-functions, defined on the grid Z^m, of the discrete Dirac operator D, involving both forward and backward…
A universal minimal spinor set of linear differential equations describing anyons and ordinary integer and half-integer spin fields is constructed with the help of deformed Heisenberg algebra with reflection. The construction is generalized…
Local decompositions of a Dirac spinor into `charged' and `real' pieces psi(x) = M(x) chi(x) are considered. chi(x) is a Majorana spinor, and M(x) a suitable Dirac-algebra valued field. Specific examples of the decomposition in 2+1…
The decomposition of the spinor bundle of the spin Grassmann manifolds $G_{m,n}=SO(m+n)/SO(m)\times SO(n)$ into irreducible representations of $\mathfrak{so}(m)\oplus\mathfrak{so}(n)$ is presented. A universal construction is developed and…
Let G be a compact, semi-simple Lie group and H a maximal rank reductive subgroup. The irreducible representations of G can be constructed as spaces of harmonic spinors with respect to a Dirac operator on the homogeneous space G/H twisted…
The existence of decompositions of the form $f=P\cdot q+r$ with $P_k^{\ast}\left( D\right) r=0$, where $f$ is entire, $P$ a polynomial and $P^{\ast}_k$ the principal part of $P$ with its coefficients conjugated, was achieved in…
The issue of general covariance of spinors and related objects is reconsidered. Given an oriented manifold $M$, to each spin structure $\sigma$ and Riemannian metric $g$ there is associated a space $S_{\sigma, g}$ of spinor fields on $M$…
A complete effective Hamiltonian for relativistic corrections at orders $m\alpha^6$ and $m\alpha^6(m/M)$ in a one-electron molecular system is derived from the NRQED Lagrangian. It includes spin-independent corrections to the energy levels…
This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin $(j > 1/2)$ using chiral representations of the Lorentz group, i.e. the $(j,0)$ and $(0,j)$ representations and their…