The Clifford algebra of a n-dimensional Euclidean vector space provides a general language comprising vectors, complex numbers, quaternions, Grassman algebra, Pauli and Dirac matrices. In this work, we present an introduction to the main ideas of Clifford algebra, with the main goal to develop a package for Clifford algebra calculations for the computer algebra program Mathematica∗. The Cliffor...

The Dirac equation is not semisimple. We therefore construct it as a contraction of a simple theory. The underlying simple structure is necessarily purely algebraic and non-local. It consists of many isomorphic distinguishable qubits with Clifford-Wilczek statistics and spin h̄/2, having a Clifford algebra with 6N generators as algebra of observables. The quantum imaginary ih̄ arises as the vacuu...

This is a book for those who would like to learn something about special and general relativity beyond the usual textbooks, about quantum field theory, the elegant Fock-Schwinger-Stueckelberg proper time formalism, the elegant description of geometry by means of Clifford algebra, about the fascinating possibilities the latter algebra offers in reformulating the existing physical theories, and q...

A novel Chern-Simons E8 gauge theory of Gravity in D = 15 based on an octic E8 invariant expression in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of gravity with the other forces is very plausible within the framework of a supersymmetric extension (to incorporate spacetime fermions) of this Chern-Simons E8 gauge theory. We review the constru...

The Clifford algebraic formulation of the Duffin–Kemmer–Petiau (DKP) algebras is applied to recast De Donder–Weyl Hamiltonian (DWH) theory as an description independent matrix representation DKP algebra. We show that DWH equations for antisymmetric fields arise out action algebra on certain invariant subspaces which carry representations fields. representation-free formula bracket associated wi...

In  this paper we define the $p$-analog of the restericted reperesentations and also the $p$-analog of the Fourier--Stieltjes algebras on the inverse semigroups . We improve some results about Herz algebras on Clifford semigroups. At the end of this paper we give the necessary and sufficient condition for amenability of these algebras on Clifford semigroups.