Related papers: On perturbations of Dirac operators with variable …
We study the notion of a Dirac operator in the framework of twist-deformed noncommutative geometry. We provide a number of well-motivated candidate constructions and propose a minimal set of axioms that a noncommutative Dirac operator…
In this article, we provide the spectral analysis of a Dirac-type operator on $\mathbb{Z}^2$ by describing the behavior of the spectral shift function associated with a sign-definite trace-class perturbation by a multiplication operator. We…
Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double…
We study the spectrum and dynamics of a one-dimensional discrete Dirac operator in a random potential obtained by damping an i.i.d. environment with an envelope of type $n^{-\alpha}$ for $\alpha>0$. We recover all the spectral regimes…
We prove that limit-periodic Dirac operators generically have spectra of zero Lebesgue measure and that a dense set of them have spectra of zero Hausdorff dimension. The proof combines ideas of Avila from a Schr\"odinger setting with a new…
The aim of this paper is to construct an explicit potential for the Dirac operator that has purely singular continuous spectrum. The characteristic trait of this potential is that it consists of bumps whose distance is growing rapidly. This…
In this paper we present a complete spectral analysis of Dirac operators with non-Hermitian matrix potentials of the form $i\operatorname{sgn}(x)+V(x)$ where $V\in L^1$. For $V=0$ we compute explicitly the matrix Green function. This allows…
We consider a two-dimensional massless Dirac operator coupled to a magnetic field $B$ and an electric potential $V$ growing at infinity. We find a characterization of the spectrum of the resulting operator $H$ in terms of the relation…
We investigate the spectral consequences of the uniquely determined Hermitian ordering of the Dirac Hamiltonian with spatially varying mass. In contrast to the nonrelativistic case, where continuous families of admissible prescriptions…
The aim of this paper is to study the existence of eigenvalues in the gap of the essential spectrum of the one-dimensional Dirac operator in the presence of a bounded potential. We employ a generalized variational principle to prove…
This is the last paper in a series of three in which we have studied the Peierls substitution in the case of a weak magnetic field. Here we deal with two $2d$ Bloch eigenvalues which have a conical crossing. It turns out that in the…
The Dirac equation in a curved spacetime depends on a field of coefficients (essentially the Dirac matrices), for which a continuum of different choices are possible. We study the conditions under which a change of the coefficient fields…
Let $H_0$ be a purely absolutely continuous selfadjoint operator acting on some separable infinite-dimensional Hilbert space and $V$ be a compact non-selfadjoint perturbation. We relate the regularity properties of $V$ to various spectral…
We develop the method of similar operators to study the spectral properties of unbounded perturbed linear operators that can be represented by matrices of various kinds. The class of operators under consideration includes various…
Effects of dynamical quarks on the microscopic spectrum of the Wilson Dirac operator are analyzed by means of effective field theory. We consider the distributions of the real modes of the Wilson Dirac operator as well as the spectrum of…
It is shown that the eigenvalue problem for the hermitian Wilson-Dirac operator of for a uniform magnetic field in two dimensions can be reduced to one-dimensional problem described by a relativistic analog of the Harper equation. An…
This paper is devoted to the study of the spectral properties of Dirac operators on the three-sphere with singular magnetic fields supported on smooth, oriented links. As for Aharonov-Bohm solenoids in Euclidean three-space, the flux…
We study the spectral problem for the Dirac operator with degenerate boundary conditions and a complex-valued summable potential. Sufficient conditions are found under which the spectrum of the problem under consideration coincides with the…
We analyse spectral properties of a class of compact perturbations of block Toeplitz operators associated with analytic symbols. In particular, a limiting absorption principle and the absence of singular continuous spectrum are shown. The…
Dirac's formulation of magnetic monopoles is shown to be equivalent to Maxwell theory coupled to 2-form gauge fields so that it has a local 1-form symmetry, with the 2-form gauge fields given in terms of the 2-form current densities…