相关论文: The kernel of Dirac operators on $\S^3$ and $\R^3$
Metaplectic operators form a relevant class of operators appearing in different applications, in the present work we study their Schwartz kernels. Namely, diagonality of a kernel is defined by imposing rapid off-diagonal decay conditions,…
The radially deformed Fourier transform, introduced in [S. Ben Said, T. Kobayashi and B. Orsted, Laguerre semigroup and Dunkl operators, Compositio Math.], is an integral transform that depends on a numerical parameter $a \in R^{+}$. So…
This paper deals with the massive three-dimensional Dirac operator coupled with a Lorentz scalar shell interaction supported on a compact smooth surface. The rigorous definition of the operator involves suitable transmission conditions…
The "square root" of the Dirac operator derived on the superspace is used to construct supersymmetric field equations. In addition to the recently found solution - a vector supermultiplet I demonstrate how a chiral supermultiplet follows as…
We apply the theory of de Branges-Rovnyak spaces to describe kernels of some Toeplitz operators on the classical Hardy space $H^2$. In particular, we discuss the kernels of the operators $T_{\bar f/ f}$ and $T_{\bar I\bar f/ f}$, where $f$…
The adjoint of a matrix in the Lie algebra associated with a matrix algebra is a fundamental operator, which can be generalized to a more general operator $\varphi_{AB}: X\rightarrow AX-XB$ by two matrices $A$ and $B$. The kernel of the…
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while…
We show that the eigenspaces of the Dirac operator $H=\alpha\cdot (D - A(x)) + m \beta $ at the threshold energies $\pm m$ are coincide with the direct sum of the zero space and the kernel of the Weyl-Dirac operator $\sigma\cdot (D -…
We introduce a three-dimensional random point field using the concept of the quaternion determinant. Orthogonal polynomials on the space of pure quaternions are defined, and used to construct a kernel function similar to the Ginibre kernel.…
In this article, we study the spectrum of the magnetic Dirac operator, and the magnetic Dirac operator with potential over complete Riemannian manifolds. We find sufficient conditions on the potentials as well as the manifold so that the…
We introduce the notion of multiplication kernels of birational and $D$-module type and give various examples. We also introduce the notion of a semi-classical multiplication kernel associated with an integrable system and discuss its…
We present the properties of new Dirac-type operators generated by real or complex-valued special Killing-Yano tensors that are covariantly constant and represent roots of the metric tensor. In the real case these are just the so called…
Magnetic fields are important for accretion disc structure. Magnetic fields in a disc system may be transported with the accreted matter. They can be associated with either the central body and/or jet, and be fossil or dynamo excited in…
We study the Bergman kernel of certain domains in $\mathbb{C}^n$, called elementary Reinhardt domains, generalizing the classical Hartogs triangle. For some elementary Reinhardt domains, we explicitly compute the kernel, which is a rational…
The article deals with intrinsic metrics, Dirac operators and spectral triples induced by regular Dirichlet and resistance forms. We show, in particular, that if a local resistance form is given and the space is compact in resistance…
We prove that canonical Dirac expression with linear potential generates operators on axis and half axis, for which we can find the eigenvalues and eigenfunctions in explicit form. We construct the perturbations of these operators with in…
We use supersymmetry transformations to obtain new one parameter family of inhomogeneous magnetic fields $\mathbf{B} = \widetilde{\mathcal{B}}(x,\lambda) \hat{e}_z$ for which the massless Dirac electron possesses exact solution. The…
The geometric kernel (or simply the kernel) of a polyhedron is the set of points from which the whole polyhedron is visible. Whilst the computation of the kernel for a polygon has been largely addressed in the literature, fewer methods have…
We give an explicit integral formula for the Dunkl kernel associated to root system of type $A_2$ and parameter $k>0$, by exploiting recent result in [1].
This is a short review of two-dimensional Dirac fermions in graphene and similar systems such as boron nitride, quasi-2D organic salts $\alpha$-(BEDT-TTF)$_2$I$_3$, artificial graphene with cold atoms in optical lattices, etc. The emphasis…