Related papers: A universal Dirac operator and noncommutative spin…
We construct the Calderon projection on the space of Cauchy datas for a twisted Dirac operator in the Mischenko--Fomenko pseudodifferential calculus for operators acting on bundles of finitely generated $C^*$--Hilbert modules on a compact…
In this paper, we give two Lichnerowicz type formulas for Dirac operators and signature operators twisted by a vector bundle with a non-unitary connection. We also prove two Kastler-Kalau-Walze type theorems for twisted Dirac operators and…
In this paper, we compute the spectral Einstein functional associated with the Dirac operator with torsion on even-dimensional spin manifolds without boundary.
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…
We prove the universality of correlation functions of chiral unitary and unitary ensembles of random matrices in the microscopic limit. The essence of the proof consists in reducing the three-term recursion relation for the relevant…
In this paper, we consider the eigenvalue problem of Dirac operator on a compact Riemannian manifold isometrically immersed into Euclidean space and derive some extrinsic estimates for the sum of arbitrary consecutive $n$ eigenvalues of the…
Spectral triples describe and generalize Riemannian spin geometries by converting the geometrical information into algebraic data, which consist of an algebra $A$, a Hilbert space $H$ carrying a representation of $A$ and the Dirac operator…
We compute eta invariants of various Dirac type operators on circle bundles over Riemann surfaces via two approaches: an adiabatic approach based on the results of Bismut-Cheeger-Dai and a direct elementary one. These results, coupled with…
We find all spin operators for a Dirac particle satisfying the following very general conditions: (i) spin does not convert positive (negative) energy states into negative (positive) energy states, (ii) spin is a pseudo-vector, and (iii)…
Let M be a closed spin manifold of dimension at least three with a fixed topological spin structure. For any Riemannian metric, we can construct the associated Dirac operator. The spectrum of this Dirac operator depends on the metric of…
Using Liu's modular invariance method and its odd-dimensional extension by Han and Yu, we establish new Witten rigidity theorems for the generalized Witten genus of twisted Dirac operators on even-dimensional spin$^c$ manifolds and twisted…
We analyze the limit of the spectrum of a geometric Dirac-type operator under a collapse with bounded diameter and bounded sectional curvature. In the case of a smooth limit space B, we show that the limit of the spectrum is given by the…
We establish a lower bound for the eigenvalues of the Dirac operator defined on a compact K\"ahler-Einstein manifold of positive scalar curvature and endowed with particular ${\rm spin}^c$ structures. The limiting case is characterized by…
We review a procedure of factorizing the Minkowski space Dirac operator over a~suitable superspace, discuss its Euclidean space version and apply the worked out formalism in the case od an almost-commutative Dirac operator. The presented…
In this second part of the paper, we define spectral spacetimes, a noncommutative generalization of Lorentzian orientable spacetimes of even dimension with a spin structure. There are two main differences with spectral triples: the…
Based on the relation to random matrix theory, exact expressions for all microscopic spectral correlators of the Dirac operator can be computed from finite-volume partition functions. This is illustrated for the case of $SU(N_c)$ gauge…
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…
The aim of this paper is to study a possible "boundary phenomenon" for Spinc Dirac operators in a special case. If you parametrise Spinc Dirac operators by a family of connections on a Spinc 4-manifold with boundary, this boundary inherits…
The q-deformed fuzzy Dirac and chirality operators on quantum fuzzy four-sphere $ S^{4}_{qF} $. Using the q-deformed fuzzy Ginsparg-Wilson algebra, it has been studied the q-deformed fuzzy Dirac and chirality operators in instanton and…
In this paper, we derive some spectral (0,4)-tensor functionals by four one-forms and the Dirac operator and the noncommutative residue on even-dimensional compact spin manifolds without boundary. Then, we extend these spectral (0,4)-tensor…