Related papers: Dirac operator on the quantum fuzzy four-sphere $ …
All microscopic correlation functions of the spectrum of the Hermitian Wilson Dirac operator with any number of flavors with equal masses are computed. In particular, we give explicit results for the spectral density in the physical case…
We study spectral triples over noncommutative principal U(1)-bundles of arbitrary dimension and formulate a compatibility condition between the connection and the Dirac operator on the total space and on the base space of the bundle.…
We reconsider constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature. To avoid possible ultra-violet(UV) divergences, we work on a lattice, employing the overlap Dirac…
We define U(n) gauge theory on fuzzy S^2_N x S^2_N as a multi-matrix model, which reduces to ordinary Yang-Mills theory on S^2 x S^2 in the commutative limit N -> infinity. The model can be used as a regularization of gauge theory on…
We introduce non-commutative algebras, which can be associated with the function algebra of functions on a finite or half-finite cylinder. The algebras, which depend on a deformation parameter, are crossed product algebras of a partial…
We study the two-dimensional Dirac operator with an arbitrary combination of electrostatic and Lorentz scalar $\delta$-interactions of constant strengths supported on a smooth closed curve. For any combination of the coupling constants a…
We find a unique torsion free Riemannian spin connection for the natural Killing metric on the quantum group $C_q[SL_2]$, using a recent frame bundle formulation. We find that its covariant Ricci curvature is essentially proportional to the…
Starting with a Dirac operator on a configuration space of $SU(2)$ gauge connections we consider its fluctuations with inner automorphisms. We show that a certain type of twisted inner fluctuations leads to a Dirac operator whose square…
We consider Dolbeault-Dirac operators on quantized irreducible flag manifolds as defined by Kr\"ahmer and Tucker-Simmons. We show that, in general, these operators do not satisfy a formula of Parthasarathy-type. This is a consequence of two…
We summarize a recent work on the subject title. 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…
In a dynamical lattice simulation with the overlap Dirac operator and $N_f=2$ mass degenerate quarks we study all possible $J=0$ and $J=1$ correlators upon exclusion of the low lying "quasi-zero" modes from the valence quark propagators.…
We investigate $L^1\to L^\infty$ dispersive estimates for the Dirac equation with a potential in four spatial dimensions. We classify the structure of the obstructions at the thresholds as being composed of an at most two dimensional space…
We simulate Quantum Chromodynamics in four Euclidean dimensions with two (degenerate mass) flavors of dynamical quarks. The Dirac operator is the so-called chirally improved operator that has been studied so far in quenched calculations. We…
We reinvestigate constraints on the eigenvalue density of the Dirac operator in the chiral symmetric phase of 2 flavor QCD at finite temperature, employing the overlap Dirac operator with the exact chiral symmetry at finite lattice spacings…
We analyze the parabolic Dirac operator $D \pm i\partial_t$ in a biquaternionic setting, characterizing its kernel via generalized div-curl systems and Cauchy-Riemann-type relations between the real and imaginary parts. Using the machinery…
It will be shown that the defining relations for fuzzy torus and deformed (squashed) sphere proposed by J. Arnlind, et al (hep-th/0602290) (ABHHS) can be rewriten as a new algebra which contains q-deformed commutators. The quantum parameter…
Non-commutative Quantum Mechanics in 3D is investigated in the framework of the abelian Drinfeld twist which deforms a given Hopf algebra while preserving its Hopf algebra structure. Composite operators (of coordinates and momenta) entering…
The lattice studies in QCD demonstrate the nontrivial localization behavior of the eigenmodes of the 4D Euclidean Dirac operator considered as Hamiltonian of $4+1$ dimensional disordered system. We use the holographic viewpoint to provide…
We describe how it is possible to describe irreducible actions of the Hodge - de Rham Dirac operator upon the exterior algebra over the quantum spheres ${\rm SU}_q(2)$ equipped with a three dimensional left covariant calculus.
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…