Related papers: Koszul complexes, Birkhoff normal form and the mag…
We study the resolvent kernel (Green's function) of magnetic Dirac operators on a half-plane with boundary conditions interpolating between infinite mass and zigzag cases, excluding the latter. We show that these kernels have all the…
We explore a new simple N=2 SQM model describing the motion over complex manifolds in external gauge fields. The nilpotent supercharge Q of the model can be interpreted as a (twisted) exterior holomorphic derivative, such that the model…
We give an improvement of sharp Berezin type bounds on the Riesz means $\sum_k(\Lambda-\lambda_k)_+^\sigma$ of the eigenvalues $\lambda_k$ of the Dirichlet Laplacian in a domain if $\sigma\geq 3/2$. It contains a correction term of the…
We define two types of pseudo-differential perturbations of the Dirac operator within the framework of the noncommutative geometry. And we obtain the noncommutative residue of the inverse square of these perturbations on 4-dimensional…
We consider magnetic fields on $\mathbb{R}^3$ which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic field cannot have a zero mode. In particular…
In this work we study Dirac operators on two-dimensional domains coupled to a magnetic field perpendicular to the plane. We focus on the infinite-mass boundary condition (also called MIT bag condition). In the case of bounded domains, we…
In this paper, which is a follow-up of our first paper "Normal forms for ordinary differential operators, I", we extend the theory of normal forms for non-commuting operators, and obtain as an application a commutativity criterion for…
We aim at constructing an analog of the Weyl calculus in an infinite dimensional setting, in which the usual configuration and phase spaces are ultimately replaced by infinite dimensional measure spaces, the so-called abstract Wiener…
By making use of the Kubo formula, we calculate the conductivity of Dirac and Weyl semimetals in a magnetic field. We find that the longitudinal (along the direction of the magnetic field) magnetoresistivity is negative at sufficiently…
In this work we consider the $\eta$-invariant for pseudodifferential operators of tensor product type, also called bisingular pseudodifferential operators. We study complex powers of classical bisingular operators. We prove the trace…
This paper is devoted to semiclassical estimates of the eigenvalues of the Pauli operator on a bounded open set whose boundary carries Dirichlet conditions. Assuming that the magnetic field is positive and a few generic conditions, we…
Dirac's ket-bra formalism is the "language" of quantum mechanics and quantum field theory. In Refs.(Fan et al, Ann. Phys. 321 (2006) 480; 323 (2008) 500) we have reviewed how to apply Newton-Leibniz integration rules to Dirac's ket-bra…
We use the averaged variational principle introduced in a recent article on graph spectra [7] to obtain upper bounds for sums of eigenvalues of several partial differential operators of interest in geometric analysis, which are analogues of…
For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal…
In a series of papers we have argued that the 'basic' physical procedure of minimal coupling giving the quantum description of a Hamiltonian system interacting with a magnetic field, can be given a very satisfactory mathematical formulation…
Inverse problem for Dirac systems with locally square summable potentials and rectangular Weyl functions is solved. For that purpose we use a new result on the linear similarity between operators from a subclass of triangular integral…
A self-consistent construction of the overlap lattice Dirac operator coupled to chiral chemical potential is proposed. With the help of the constructed operator we compute electric current induced by a constant magnetic field (Chiral…
We provide a comprehensive lattice formulation of various types of the Dirac operator indices, employing $K$-theory to classify the Wilson Dirac operator via its spectral flow. In contrast to the index of the overlap Dirac operator defined…
The Weyl-Wigner formalism for evaluating the intrinsic information of Dirac bispinors as correlated qubits (localized) in a magnetic field is investigated in the extension to statistical ensembles. The confining external field quantizes the…
Basically (2 + 1) dimensional Dirac equation with real deformed Lorentz scalar potential is investi gated in this study. The position dependent Fermi velocity function transforms Dirac Hamiltonian into a Klein-Gordon-like effective…