Related papers: Explicit Families of Spinor Representations
We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…
The Bargmann-Wigner (BW) scalar product is a particular case of a larger class of scalar products parametrized by a family of world-vectors. The choice of null and $p$-dependent world-vectors leads to BW amplitudes which behave as local…
The essentially unique torsionful version of the classical two-component spinor formalisms of Infeld and van der Waerden is presented. All the metric spinors and connecting objects that arise here are formally the same as the ones borne by…
With the help of a useful mathematical tool, the polar decomposition of closed operators, and a simple observation, i.e. the unique relation between tensor-product states and compact operators, we manage to give a compact and coherent…
This is the first paper in a series of two papers. In this paper we construct complexes of invariant differential operators which live on homogeneous spaces of $|2|$-graded parabolic geometries of some particular type. We call them…
In these notes we introduce the Clifford algebra of a quadratic space using techniques from universal algebra and algebraic theory of quadratic forms. We also define the Clifford, Pin and Spin groups associated to the algebra, and study how…
Let Cl(V,g) be the real Clifford algebra associated to the real vector space V, endowed with a nondegenerate metric g. In this paper, we study the class of Z_2-gradings of Cl(V,g) which are somehow compatible with the multivector structure…
We give an explicit bijective correspondence between between nonzero pairs of complex numbers, which we regard as spinors or spin vectors, and horospheres in 3-dimensional hyperbolic space decorated with certain spinorial directions. This…
Following the program of investigation of alternative spinor duals potentially applicable to fermions beyond the standard model, we demonstrate explicitly the existence of several well-defined spinor duals. Going further we define a mapping…
The exterior algebra of Minkowski space naturally has the structure of a sixteen-dimensional Clifford algebra representation, and so can be used as the space of spinors. We examine plane, circular, and spherical solutions to the free Dirac…
In this article we construct and discuss several aspects of the two-component spinorial formalism for six-dimensional spacetimes, in which chiral spinors are represented by objects with two quaternionic components and the spin group is…
We explore differential and algebraic operations on the exterior product of spinor representations and their twists that give rise to cohomology, the spin cohomology. A linear differential operator $d$ is introduced which is associated to a…
We suggest Clifford algebra as a useful simplifying language for present quantum dynamics. Clifford algebras arise from representations of the permutation groups as they arise from representations of the rotation groups. Aggregates using…
In this paper, we use Clifford algebra and the spinor calculus to study the complex structures on Euclidean space $R^8$ and the spheres $S^4,S^6$. By the spin representation of $G(2,8)\subset Spin(8)$ we show that the Grassmann manifold…
We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as…
In this article we present a new and not fully employed geometric algebra model. With this model a generalization of the conformal model is achieved. We discuss the geometric objects that can be represented. Furthermore, we show that the…
In this paper we examine a new class of five dimensional (5D) exact solutions in extra dimension gravity possessing Lie algebroid symmetry. The constructions provide a motivation for the theory of Clifford nonholonomic algebroids elaborated…
We study the chiral flat space higher-spin algebra, which is the global symmetry algebra of the chiral higher-spin theory in the 4d Minkowski space. We find that it can be constructed as the universal enveloping algebra of a certain chiral…
We discuss how transformations in a three dimensional euclidean space can be described in terms of the Clifford algebra $\mathcal{C}\ell_{3,3}$ of the quadratic space $\mathbb{R}^{3,3}$. We show that this algebra describes in a unified way…
This paper presents a method to build explicit tensor-train (TT) representations. We show that a wide class of tensors can be explicitly represented with sparse TT-cores, obtaining, in many cases, optimal TT-ranks. Numerical experiments…