Related papers: The Spherical $\pi$-Operator

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 $R^{n}$…

In this article, we present the symmetry group of a global slice Dirac operator and its iterated ones. Further, the explicit forms of intertwining operators of the iterated global slice Dirac operator are given. At the end, we introduce a…

Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple…

A $p$-adic Schr\"{o}dinger-type operator $D^{\alpha}+V_Y$ is studied. $D^{\alpha}$ ($\alpha>0$) is the operator of fractional differentiation and $V_Y=\sum_{i,j=1}^nb_{ij}<\delta_{x_j}, \cdot>\delta_{x_i}$ $(b_{ij}\in\mathbb{C})$ is a…

In this paper we introduce the Dirac and spin-Dirac operators associated to a connection on Riemann-Cartan space(time) and standard Dirac and spin-Dirac operators associated with a Levi-Civita connection on a Riemannian (Lorentzian)…

We study the linear topological invariant $(\Omega)$ for a class of Fr\'echet spaces of holomorphic functions of rapid decay on strip-like domains in the complex plane, defined via weight function systems. We obtain a complete…

The paper deals with the Dirac operator generated on the finite interval $[0,\pi]$ by the differential expression $-B\mathbf{y}'+Q(x)\mathbf{y}$, where $$ B=\begin{pmatrix}0&1\\-1&0\end{pmatrix},\qquad…

We obtaine the full characterization of proper closed invariant subspaces of a generalized backward shift operator (Pommiez operator) in the Frechet space of all holomorphic functions on a simply connected domain $\Omega$ of the complex…

A parametrised diffusion operator on the regular domain $\Omega$ of a $p$-adic Schottky group is constructed. It is defined as an integral operator on the complex-valued functions on $\Omega$ which are invariant under the Schottky group…

The Dirac operator d+delta on the Hodge complex of a Riemannian manifold is regarded as an annihilation operator A. On a weighted space L_mu^2 Omega, [A,A*] acts as multiplication by a positive constant on excited states if and only if the…

Let A be a cosemisimple Hopf *-algebra with antipode S and let $\Gamma$ be a left-covariant first order differential *-calculus over A such that $\Gamma$ is self-dual and invariant under the Hopf algebra automorphism S^2. A quantum Clifford…

We investigate the spin $1/2$ fermions on quantum two spheres. It is shown that the wave functions of fermions and a Dirac Operator on quantum two spheres can be constructed in a manifestly covariant way under the quantum group $SU(2)_q$.…

We describe both the Hodge - de Rham and the spin manifold Dirac operator on the spheres ${\rm S}^3$ and ${\rm S}^2$, following the formalism introduced by K\"ahler, and exhibit a complete spectral resolution for them in terms of suitably…

The fermionic topological charge of lattice gauge fields, given in terms of a spectral flow of the Hermitian Wilson--Dirac operator, or equivalently, as the index of Neuberger's lattice Dirac operator, is shown to have analogous properties…

We calculate the index of the Dirac operator defined on the q-deformed fuzzy sphere. The index of the Dirac operator is related to its net chiral zero modes and thus to the trace of the chirality operator. We show that for the q-deformed…

We establish an $L^2$-Gamma index theorem for the Dirac operator on a globally hyperbolic manifold $M$ with Cauchy hypersurface $\Sigma$ being a Galois covering of a compact smooth manifold with Galois group $\Gamma$. Our argument rewrites…

We derive a formula for the gravitational part of the spectral action for Dirac operators on 4-dimensional manifolds with totally anti-symmetric torsion. We find that the torsion becomes dynamical and couples to the traceless part of the…

It is shown that in the case of the spherically symmetric static backgrounds there is a gauge in which the Dirac equation is manifestly covariant under rotations. This allows us to separate the spherical variables like in the flat…

A Grassmann functional phase space is formulated for the definition of fermionic Wigner functionals by identifying suitable fermionic operators that are analogues to boson quadrature operators. Instead of the Majorana operators, we use…

We investigate the operator $-\Delta -\alpha \delta (x-\Gamma)$ in $L^2(\mathbb{R}^3)$, where $\Gamma$ is a smooth surface which is either compact or periodic and satisfies suitable regularity requirements. We find an asymptotic expansion…