Related papers: The kernel of Dirac operators on $\S^3$ and $\R^3$

Large magnetic fields exist in magnetars and are produced in off-central heavy-ion collisions. For the latter, field strengths are estimated to be comparable to strong interaction scales. This fact has motivated many studies of QCD physics…

Modifications of Dirac operators in supergravity flux backgrounds are considered. Modified spin curvature operators and squares of modified Dirac operators corresponding to Schr\"odinger-Lichnerowicz-like formulas are obtained for different…

Empirical observation of high dimensional phenomena, such as the double descent behaviour, has attracted a lot of interest in understanding classical techniques such as kernel methods, and their implications to explain generalization…

Kernel methods are an incredibly popular technique for extending linear models to non-linear problems via a mapping to an implicit, high-dimensional feature space. While kernel methods are computationally cheaper than an explicit feature…

The paper is devoted to Mellin convolution operators with meromorphic kernels in Bessel potential spaces. We encounter such operators while investigating boundary value problems for elliptic equations in planar 2D domains with angular…

We give a short overview of the effective action approach in quantum field theory and quantum gravity and describe various methods for calculation of the asymptotic expansion of the heat kernel for second-order elliptic partial differential…

Let k be an algebraically closed field of characteristic zero and let B be a finitely generated k-domain. We study semisimple derivations on B, with special emphasis on those whose eigenvalues are integers. For such derivations, after…

In this largely expository paper we give a self-contained treatment of the Dirac operator. Emphasizing the algebraic point of view we first sketch the necessary prerequisites from Clifford algebras and their representations and then define…

Dirac operators on curved space-times are introduced with the help of a new point-view that observers have to be included in the formulation of natural laws. The class of Dirac operators are Lorentz invariant in the sense that the…

The focus of this paper is the production of magnetic monopoles Drell-Yan and the Photon-Fusion mechanisms to generate velocity-dependent scalar, fermionic, and vector monopoles of spin angular momentum $0,\frac{1}{2},1$ respectively at a…

Dirac metals are characterized by the linear dispersion of fermionic quasi-particles, with the Dirac point hidden inside a Fermi surface. We study the magnetotransport in these materials using chiral kinetic theory to describe within the…

In this paper, we pursue the investigations started in \cite{Mas-You} where the authors provide a construction of the Dunkl intertwining operator for a large subset of the set of regular multiplicity values. More precisely, we make concrete…

We study spherically symmetric strongly gravitating configurations supported by nonlinear spinor fields and non-Abelian SU(2) Yang-Mills/Proca magnetic fields. Regular asymptotically flat solutions describing objects with positive…

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…

The use of complexified quaternions and $i$-complex geometry in formulating the Dirac equation allows us to give interesting geometric interpretations hidden in the conventional matrix-based approach.

We study a family of fractional integral operators whose kernels satisfying an non-isotropic dilation have singularity on a coordinate subspace. A characterization is given for these operators bounded from the classical, atom decomposable…

We define the notion of a co-Riemannian structure and show how it can be used to define the Dirac operator on an appropriate infinite dimensional manifold. In particular, this approach works for the smooth loop space of a so-called string…

Let M be a closed spin manifold of dimension at least three with a fixed topological spin structure. For any Riemannian metric, we can construct the associated Dirac operator. The spectrum of this Dirac operator depends on the metric of…

It is shown that for the modular representations associated to Rational Conformal Field Theories, the kernel is a congruence subgroup whose level equals the order of the Dehn-twist. An explicit algebraic characterization of the kernel is…

Dunkl operators associated with finite reflection groups generate a commutative algebra of differential-difference operators. There exists a unique linear operator called intertwining operator which intertwines between this algebra and the…