Related papers: Spectral triples with multitwisted real structure
In this paper, we introduce notions of (proto-, quasi-)twilled Lie triple systems and give their equivalent descriptions using the controlling algebra and bidegree convention. Then we construct an $L_\infty$-algebra via a twilled Lie triple…
In this paper, we consider the recovery of third-order differential operators from two spectra, as well as fourth-order or fifth-order differential operators from three spectra, where these differential operators are endowed with…
We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…
We present a theory of electronic properties and the spin blockade phenomena in a gated linear triple quantum dot. Quadruple points where four different charge configurations are on resonance, particularly involving (1,1,1) configuration,…
We introduce twisted arrow categories of operads and of algebras over operads. Up to equivalence of categories, the simplex category $\Delta$, Segal's category $\Gamma$, Connes cyclic category $\Lambda$, Moerdijk-Weiss dendroidal category…
In a recent paper we showed that a subspace of a real JBW*-triple is an M-summand if and only if it is a weak*-closed triple ideal. As a consequence, M-ideals of real JB*-triples, including real C*-algebras, real JB*-algebras and real TROs,…
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…
For a rational and $C_2$-cofinite vertex operator algebra $V$ with an automorphism group $G$ of prime order, the fusion rules for twisted $V$-modules are studied, a twisted Verlinde formula which relates fusion rules for $g$-twisted modules…
We study the semiclassical spectral theory of a one-dimensional Dirac operator describing waves at the interface between topologically distinct media. We derive a modified Bohr-Sommerfeld quantization condition for the squared operator via…
We investigate the presence of twinlike models in theories described by several real scalar fields. We focus on the first-order formalism, and we show how to build distinct scalar field theories that support the same extended solution, with…
We study higher-order analogues of Dirac structures, extending the multisymplectic structures that arise in field theory. We define higher Dirac structures as involutive subbundles of $TM+\wedge^k TM^*$ satisfying a weak version of the…
For a symplectic manifold admitting a metaplectic structure (a symplectic analogue of the Riemannian spin structure), we construct a sequence consisting of differential operators using a symplectic torsion-free affine connection. All but…
The structure of a bound state of several Dirac particles is discussed. Relying on solid mathematical arguments of the Wigner-Racah algebra, it is proved the a non-negligible number of configurations is required for a description of this…
In this paper, we introduce a class of twisted multiparameter singular integrals on $\mathbb{R}^{2m}$, motivated by the Cauchy--Szeg\H{o} projections and the solving operators for $\bar{\partial}_b$ on a broad family of quadratic surfaces…
The goal of this work is to extend Dirac-type tensor equations to a curved space. We take four 1-forms (a tetrad) as a unique structure, which determines a geometry of space-time.
We construct a two dimensional unoriented open/closed topological field theory from a finite graded group $\pi:\hat{G} \twoheadrightarrow \{1,-1\}$, a $\pi$-twisted $2$-cocycle $\hat{\theta}$ on $B \hat{G}$ and a character $\lambda: \hat{G}…
We consider the following first order systems of mathematical physics. 1.The Dirac equation with scalar potential. 2.The Dirac equation with electric potential. 3.The Dirac equation with pseudoscalar potential. 4.The system describing…
We introduce the notion of a prile of one-sided triangulated categories. Roughly speaking, a prile consists of two one-sided triangulated categories having a common full subcategory which inherits a pretriangulated structure from these…
Three-dimensional theories with cubic symmetry are studied using the machinery of the numerical conformal bootstrap. Crossing symmetry and unitarity are imposed on a set of mixed correlators, and various aspects of the parameter space are…
We characterize possible spectra of rank-one perturbations B of a self-adjoint operator A with discrete spectrum and, in particular, prove that the spectrum of B may include any number of real or non-real eigenvalues of arbitrary algebraic…