相关论文: Chirality and Dirac Operator on Noncommutative Sph…

This paper studies the K-homology of a crossed product of a discrete group acting smoothly on a manifold, with a better understanding of the noncommutative geometry of the crossed-product as the primary goal, and the Baum-Connes apparatus…

We introduce non-linear Dirac operators in $\mathbb{R}^{n}$ associated to the $p$-harmonic equation and we extend to other contexts including spin manifolds and the sphere.

We consider the problem of constrained motion along a conic path under a given external potential function. The model is described as a second-class system capturing the behavior of a certain class of specific quantum field theories. By…

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…

Equivariance under the action of Uq(so(5)) is used to compute the left regular and (chiral) spinorial representations of the algebra of the orthogonal quantum 4-sphere S^4_q. These representations are the constituents of a spectral triple…

The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…

Odd-dimensional Riemannian spaces that are non-orientable, but have a pin structure, require the consideration of the twisted adjoint representation of the corresponding pin group. It is shown here how the Dirac operator should be modified,…

In this paper, we study a singular perturbation of a problem used in dimension two to model graphene or in dimension three to describe the quark confinement phenomenon in hadrons. The operators we consider are of the form $H + M\beta V…

A Dirac operator D on quantized irreducible generalized flag manifolds is defined. This yields a Hilbert space realization of the covariant first-order differential calculi constructed by I. Heckenberger and S. Kolb. All differentials…

The discrete spectrum of the Dirac operator for a point electron in the maximal analytically extended Kerr--Newman spacetime is determined in the zero-$G$ limit (z$G$KN), under some restrictions on the electrical coupling constant and on…

The Dirac operator is considered on a bidimensional domain whose boundary carries the infinite mass boundary condition. The analysis is focused on the existence of discrete spectrum and on its asymptotic description in the thin width limit.…

We study a conformally invariant equation involving the Dirac operator and a non-linearity of convolution type. This non-linearity is inspired from the conformal Einstein-Dirac problem in dimension 4. We first investigate the compactness,…

We present examples of equivariant noncommutative Lorentzian spectral geometries. The equivariance with respect to a compact isometry group (or quantum group) allows to construct the algebraic data of a version of spectral triple geometry…

Regularization of quantum field theories (QFT's) can be achieved by quantizing the underlying manifold (spacetime or spatial slice) thereby replacing it by a non-commutative matrix model or a ``fuzzy manifold''. Such discretization by…

We construct wave functions and Dirac operator of spin $1/2$ fermions on quantum four-spheres. The construction can be achieved by the q-deformed differential calculus which is manifestly $SO(5)_q$ covariant. We evaluate the engenvalue of…

We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space $U_q(\g) \otimes \mathrm{cl}_q(\g)$ where the second tensor factor is a…

At nonzero density the eigenvalues of the Dirac operator move into the complex plane, while its singular values remain real and nonnegative. In QCD-like theories, the singular-value spectrum carries information on the diquark (or pionic)…

Quark spectra in QCD are linked to fundamental properties of the theory including the identification of pions as the Goldstone bosons of spontaneously broken chiral symmetry. The lattice Overlap-Dirac operator provides a nonperturbative,…

This work provides a first step towards the construction of a noncommutative geometry for the quantum Hall effect in the continuum. Taking inspiration from the ideas developed by Bellissard during the 80's we build a spectral triple for the…

We compute the spectrum of the Dirac operator on 3-dimensional Heisenberg manifolds. The behavior under collapse to the 2-torus is studied. Depending on the spin structure either all eigenvalues tend to $\pm\infty$ or there are eigenvalues…