Related papers: The Spherical $\pi$-Operator
A signature independent formalism is created and utilized to determine the general second-order symmetry operators for Dirac's equation on two-dimensional Lorentzian spin manifolds. The formalism is used to characterize the orthonormal…
In this paper, we develop an accurate pseudospectral method to approximate numerically the Riesz-Feller operator $D_\gamma^\alpha$ on $\mathbb R$, where $\alpha\in(0,2)$, and $|\gamma|\le\min\{\alpha, 2 - \alpha\}$. This operator can be…
We present a general method to extend results on Hilbert space operators to the Banach space setting by representing certain sets of Banach space operators $\Gamma$ on a Hilbert space. Our assumption on $\Gamma$ is expressed in terms of…
We show that, in round spheres of dimension $n\geq3$, for any given collection of codimension 2 smooth submanifolds $\mathfrak{S}:=\{\Sigma_1,...,\Sigma_N\}$ of arbitrarily complicated topology ($N$ being the complex dimension of the spinor…
This paper studies a particular class of higher order conformally invariant dif- ferential operators and related integral operators acting on functions taking values in particular finite dimensional irreducible representations of the Spin…
We introduce the space $X$ of quaternion hermitian forms of size $n$ on a ${\mathfrak p}$-adic field with odd residual characteristic, and define typical spherical functions $\omega(x;s)$ on $X$ and give their induction formula on sizes by…
We revisit the computation of the phase of the Dirac fermion scattering operator in external gauge fields. The computation is through a parallel transport along the path of time evolution operators. The novelty of the present paper compared…
This paper establishes a link between Noncommutative Geometry and canonical quantum gravity. A semi-finite spectral triple over a space of connections is presented. The triple involves an algebra of holonomy loops and a Dirac type operator…
New exact upper and lower bounds are derived on the spectrum of the square of the hermitian Wilson Dirac operator. It is hoped that the derivations and the results will be of help in the search for ways to reduce the cost of simulations…
Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma…
We give a derivation of the Dirac operator on the noncommutative $2$-sphere within the framework of the bosonic fuzzy sphere and define Connes' triple. It turns out that there are two different types of spectra of the Dirac operator and…
In this paper the spectral and scattering properties of a family of self-adjoint Dirac operators in $L^2(\Omega; \mathbb{C}^4)$, where $\Omega \subset \mathbb{R}^3$ is either a bounded or an unbounded domain with a compact $C^2$-smooth…
We consider discrete periodic operator on $\mathbb Z^d$ with respect to lattices $\Gamma\subset\mathbb Z^d$ of full rank. We describe the class of lattices $\Gamma$ for which the operator may have a spectral gap for arbitrarily small…
We numerically find out the spectrum of the $3$ spin $1$ Dirac operators found in~\cite{ApbPP}. We give an analytic and numerical proof that they are unitarily inequivalent. Since these operators come paired with an anticommuting chirality…
In this Letter, 2D Dirac oscillator in the quantum deformed framework generated by the $\kappa$-Poincar\'{e}-Hopf algebra is considered. The problem is formulated using the $\kappa$-deformed Dirac equation. The resulting theory reveals that…
Given a one-dimensional weighted Dirac operator we can define a spectral measure by virtue of singular Weyl-Titchmarsh-Kodaira theory. Using the theory of de Branges spaces we show that the spectral measure uniquely determines the Dirac…
For any triple $(M^n, g, \nabla)$ consisting of a Riemannian manifold and a metric connection with skew-symmetric torsion we introduce an elliptic, second order operator $\Omega$ acting on spinor fields. In case of a reductive space and its…
In this paper, we introduce q,{\omega}-Dirac system. We investigate the existence and uniqueness of solutions for this system and obtain some spectral properties based on the Hahn difference operator. Also we give two examples, which…
We construct a one-parameter family of algebras consisting of Fourier integral operators. We derive boundedness results, composition rules, and the spectral invariance of this class of operators. The operator algebra is defined by the decay…
We construct a 3^+ summable spectral triple (A(SU_q(2)),H,D) over the quantum group SU_q(2) which is equivariant with respect to a left and a right action of U_q(su(2)). The geometry is isospectral to the classical case since the spectrum…