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The Drazin index is a fundamental invariant in the analysis of singular matrices and their generalized inverses. While sharp results are available for block triangular matrices, the corresponding theory for anti-triangular block matrices is…

We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained.

We study quantum analogs of the Dirac type operator $-2\bar{z}\frac{\partial}{\partial\bar{z}}$ on the punctured disk, subject to the Atiyah-Patodi-Singer boundary conditions. We construct a parametrix of the quantum operator and show that…

We obtain and analyze equations determining first-order differential symmetry operators with matrix coefficients for the Dirac equation with an external electromagnetic potential in a $(2+1)$-dimensional Riemann (curved) spacetime.…

We study spectral triples over noncommutative principal U(1) bundles. Basing on the classical situation and the abstract algebraic approach, we propose an operatorial definition for a connection and compatibility between the connection and…

We prove the Bari-Markus property for spectral projectors of non-self-adjoint Dirac operators on a finite interval with square-integrable matrix-valued potentials and some separated boundary conditions.

We calculate non-singlet quark operator matrix elements of deep-inelastic scattering in the chiral limit including operators with total derivatives. This extends previous calculations with zero-momentum transfer through the operator vertex…

The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…

Using Weitzenb\"ock techniques on any compact Riemannian spin manifold we derive inequalities that involve a real parameter and join the eigenvalues of the Dirac operator with curvature terms. The discussion of these inequalities yields…

We consider the space-fractional operator with order $0<\alpha<1$ on the metric star graph. The boundary conditions at the vertices of the metric star graph providing the self-adjointness of the operator are derived. The obtained result is…

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…

We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector which may…

Kock [Bull. Austral. Math. Soc., 25 (1982), 357-386] has considered differential forms with values in a group in a context where neighborhood relations are available. By doing so, he has made it clear where the so-called Maurer-Cartan…

Assume that the compact Riemannian spin manifold $(M^n,g)$ admits a $G$-structure with characteristic connection $\nabla$ and parallel characteristic torsion ($\nabla T=0$), and consider the Dirac operator $D^{1/3}$ corresponding to the…

We describe a topological predual to differential forms constructed as an inductive limit of a sequence of Banach spaces. This subspace of currents has nice properties, in that Dirac chains and polyhedral chains are dense, and its operator…

This article is one of a series of papers. For this decade, the Dirac operator on a submanifold has been studied as a restriction of the Dirac operator in $n$-dimensional euclidean space $\EE^n$ to a surface or a space curve as physical…

In this paper, we define lower dimensional volumes of compact Riemannian manifolds with boundary. For five dimensional spin manifolds with boundary, we prove a Kastler-Kalau-Walze type theorem associated with one-form perturbations of Dirac…

We derive a number of spectral results for Dirac operators in geometrically nontrivial regions in $\mathbb{R}^2$ and $\mathbb{R}^3$ of tube or layer shapes with a zigzag type boundary using the corresponding properties of the Dirichlet…

We determine the anomalous dimension matrix for the transversity operator mixing into total derivative operators in the limit of a large number of quark flavors $n_f$ to fourth order in the strong coupling $\alpha_s$ in the…

In his book Mickelsson notices that the infinite-dimensional Grassmannian manifold of Segal and Wilson admits a Spin^c structure and after this he naturally considers the problem of defining a Dirac operator on it. Mickelsson gives a…