Related papers: Dirac operator on noncommutative principal circle …
This paper surveys a bootstrap framework for random Dirac operators arising from finite spectral triples in noncommutative geometry. Motivated by a toy model for quantum gravity to replace integration over metrics by integration over Dirac…
Investigating properties of two-dimensional Dirac operators coupled to an electric and a magnetic field (perpendicular to the plane) requires in general unbounded (vector-) potentials. If the system has a certain symmetry, the fields can be…
Let $\mathbf{A}$ be a bounded self-adjoint operator on a separable Hilbert space $\mathfrak{H}$ and $\mathfrak{H}_0\subset\mathfrak{H}$ a closed invariant subspace of $\mathbf{A}$. Assuming that $\mathfrak{H}_0$ is of codimension 1, we…
We review recent progress in the analytic study of random matrix models suggested by noncommutative geometry. One considers fuzzy spectral triples where the space of possible Dirac operators is assigned a probability distribution. These…
In this paper, under some integrability condition, we prove that an electrical perturbation of the discrete Dirac operator has purely absolutely continuous spectrum for the one dimensional case. We reduce the problem to a non-self-adjoint…
We construct spectral triples and, in particular, Dirac operators, for the algebra of continuous functions on certain compact metric spaces. The triples are countable sums of triples where each summand is based on a curve in the space.…
In this paper, we introduce the spectral Einstein functional for perturbations of Dirac operators on manifolds with boundary. Furthermore, we provide the proof of the Dabrowski-Sitarz-Zalecki type theorems associated with the spectral…
Within the framework of augmented version of the superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive the superspace unitary operator (and its Hermitian conjugate) in the context of four (3 + 1)-dimensional (4D)…
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 construct a spectral-triple framework for a noncommutative planar system associated with a fixed nondegenerate irreducible unitary sector of the kinematical symmetry group $G_{\mathrm{NC}}$, labelled by central parameters…
A Dirac operator D on the standard Podles sphere is defined and investigated. It yields a spectral triple such that |D|^{-z} is of trace class for Re z>0. Commutators with the Dirac operator give the distinguished 2-dimensional covariant…
A review of the applications of noncommutative geometry to a systematic formulation of duality symmetries in string theory is presented. The spectral triples associated with a lattice vertex operator algebra and the corresponding…
We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…
We construct new families of spectral triples over quantum spheres, with a particular attention focused on the standard Podles quantum sphere and twisted Dirac operators.
In this paper, we study the spectrality of the non-self-adjoint Dirac operator L(Q) with a complex-valued periodic matrix potential Q. We establish a condition on the off-diagonal elements of the matrix Q under which L(Q) is an…
Commutative rings of one-dimensional difference operators of rank l>1 and their deformations are effectively constructed. Our analytical constructions are based on the so-called ''Tyurin parameters'' for the stable framed holomorphic vector…
Quantum dynamical lower bounds for continuous and discrete one-dimensional Dirac operators are established in terms of transfer matrices. Then such results are applied to various models, including the Bernoulli-Dirac one and, in contrast to…
We consider an elliptic self-adjoint first order differential operator acting on pairs (2-columns) of complex-valued half-densities over a connected compact 3-dimensional manifold without boundary. The principal symbol of our operator is…
We analyse the normalisable zero-modes of the Dirac operator on the Taub-NUT manifold coupled to an abelian gauge field with self-dual curvature, and interpret them in terms of the zero modes of the Dirac operator on the 2-sphere coupled to…
After recalling Snyder's idea of using vector fields over a smooth manifold as `coordinates on a noncommutative space', we discuss a two dimensional toy-model whose `dual' noncommutative coordinates form a Lie algebra: this is the well…