Related papers: Dirac-Connes Operator on Discrete Abelian Groups a…
The paper concerns with infinite symmetric block Jacobi matrices $\bf J$ with $p\times p$-matrix entries. We present new conditions for general block Jacobi matrices to be selfadjoint and have discrete spectrum. In our previous papers there…
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…
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…
A new class of lattice Dirac operators $D$ have been recently proposed on the basis of the generalized Ginsparg-Wilson relation, $\gamma_5(\gamma_5 D) + (\gamma_5 D)\gamma_5 =2a^{2k+1}(\gamma_5 D)^{2k+2}$, where $k$ is a non-negative…
An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is…
In this thesis, we show the existence of a sequence of differential operators starting with with the Dirac operator in k Clifford variables, $D=(D_1,..., D_k)$, where $D_i=\sum_j e_j\cdot \partial_{ij}: C^\infty((\R^n)^k,\S)\to…
We study the spectrum properties for a recently constructed fixed point lattice Dirac operator. We also consider the problem of the extraction of the fermion condensate, both by direct computation, and through the Banks-Casher formula by…
The problem of self-adjoint extensions of Dirac-type operators in manifolds with boundaries is analysed. The boundaries might be regular or non-regular. The latter situation includes point-like interactions, also called delta-like…
This paper is devoted to the analysis of the single layer boundary integral operator $\mathcal{C}_z$ for the Dirac equation in the two- and three-dimensional situation. The map $\mathcal{C}_z$ is the strongly singular integral operator…
Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often…
We analyze general solutions of the Ginsparg-Wilson relation for lattice Dirac operators and formulate a necessary condition for such operators to have non-zero index in the topologically nontrivial background gauge fields.
We discuss the steps to construct Dirac operators which have arbitrary fermion offsets, gauge paths, a general structure in Dirac space and satisfy the basic symmetries (gauge symmetry, hermiticity condition, charge conjugation, hypercubic…
We give a necessary condition and a sufficient condition on the Banach lattices E and F so that an operator from E to F is DW-compact whenever its adjoint is DW-compact. We do the same, with different conditions, for DW-DP operators.…
We present a simple tool to perform analysis with groups such as SL(n,R) and SL(n,Z), that has been introduced by Vincent Lafforgue in his study of non-unitary representations, in connection with the Baum-Connes conjecture and strong…
In the present paper, we prove an abstract functional analytic criterion for a class of linear partial differential operators acting on a domain $\Omega\subseteq\Bbb R^n$ which are elliptic in the interior to have compact resolvent. This…
We give a framework of localization for the index of a Dirac-type operator on an open manifold. Suppose the open manifold has a compact subset whose complement is covered by a family of finitely many open subsets, each of which has a…
Ellipticity of boundary value problems is characterized in terms of the Calderon projector. The presence of topological obstructions for the chiral Dirac operator under local boundary conditions in even dimension is discussed. Functional…
We have considered non-magnetic materials with weak spin-orbit coupling, that are periodic in two non-collinear directions, and finite in third, orthogonal direction. In some cases, combined time-reversal and crystal symmetry of such…
We introduce the notion of a differential operator on C*-algebras. This is a noncommutative analogue of a differential operator on a smooth manifold. We show that the common closed domain of all differential operators is closed under smooth…
In this note the three dimensional Dirac operator $A_m$ with boundary conditions, which are the analogue of the two dimensional zigzag boundary conditions, is investigated. It is shown that $A_m$ is self-adjoint in…