Related papers: Geometric tri-product of the spin domain and Cliff…

The geometric calculus based on Clifford algebra is a very useful tool for geometry and physics. It describes a geometric structure which is much richer than the ordinary geometry of spacetime. A Clifford manifold (C-space) consists not…

We factorize the space-time coordinates of Minkowski space into Weyl spinors with components in a split Clifford algebra. Poisson brackets are defined for spinor-valued canonical variables and applied to the quantization of point particles…

We consider "gauge invariant" operators in Sym^N T^4, the symmetric product orbifold of N copies of the 2d supersymmetric sigma model with T^4 target. We discuss a spin chain representation for single-cycle operators and study their two…

We provide a geometric interpretation of the formulas for Steenrod's $\cup_i$ products, giving an explicit construction for a conjecture of Thorngren. We construct from a simplex and a branching structure a special frame of vector fields…

It is first shown that the scalar product on any orthogonal space (V, g) allows one to define linear isomorphisms of the vector spaces of bivectors and 2-forms on V with the underlying vector spaces of the Lie algebra so(p, q) and its dual,…

This paper is meant to be an informative introduction to spinor representations of Clifford algebras. In this paper we will have a look at Clifford algebras and the octonion algebra. We begin the paper looking at the quaternion algebra…

Transformation properties of Dirac equation correspond to Spin(3,1) representation of Lorentz group SO(3,1), but group GL(4,R) of general relativity does not accept a similar construction with Dirac spinors. On the other hand, it is…

$CPT$ groups of higher spin fields are defined in the framework of automorphism groups of Clifford algebras associated with the complex representations of the proper orthochronous Lorentz group. Higher spin fields are understood as the…

Quaternionic representations of Coxeter (reflection) groups of ranks 3 and 4, as well as those of E_8, have been used extensively in the literature. The present paper analyses such Coxeter groups in the Clifford Geometric Algebra framework,…

Given a semisimple compact Lie group $G$ and a nonzero dominant integral weight $\lambda$, the highest weight $G_q$-modules $V_{n\lambda}$ form a subproduct system of finite dimensional Hilbert spaces. Using a conjectural asymptotic…

The Clifford spectrum is a form of joint spectrum for noncommuting matrices. This theory has been applied in photonics, condensed matter and string theory. In applications, the Clifford spectrum can be efficiently approximated using…

The machinery of noncommutative geometry is applied to a space of connections. A noncommutative function algebra of loops closely related to holonomy loops is investigated. The space of connections is identified as a projective limit of…

In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…

These are lecture notes for a course on the theory of Clifford algebras, with special emphasis on their wide range of applications in mathematics and physics. Clifford algebra is introduced both through a conventional tensor algebra…

I apply the algebraic framework developed in arXiv:1101.4542 to study geometry of elliptic spaces in 1, 2, and 3 dimensions. The background material on projectivised Clifford algebras and their application to Cayley-Klein geometries is…

Here I present a full list with all possibles products between the generators of the Clifford algebra in a four-dimensional spacetime. The resulting expressions turned out to be very simple and easy to deal with.

Supergroups are defined in the framework of $\dZ_2$-graded Clifford algebras over the fields of real and complex numbers, respectively. It is shown that cyclic structures of complex and real supergroups are defined by Brauer-Wall groups…

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states $\mathbf{P}$ -- i.e., the set of one-dimensional projections on a complex Hilbert space $H$ -- and the…

In the traditional approaches to Clifford algebras, the Clifford product is evaluated by recursive application of the product of a one-vector (span of the generators) on homogeneous i.e. sums of decomposable (Grassmann), multivectors and…

Motivated by work of the first author, this paper studies symplectic embedding problems of lagrangian products that are sufficiently symmetric. In general, lagrangian products arise naturally in the study of billiards. The main result of…