Related papers: Clifford Space as a Generalization of Spacetime: P…

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…

A new theory is considered according to which extended objects in $n$-dimensional space are described in terms of multivector coordinates which are interpreted as generalizing the concept of centre of mass coordinates. While the usual…

We start from a new theory (discussed earlier) in which the arena for physics is not spacetime, but its straightforward extension-the so called Clifford space ($C$-space), a manifold of points, lines, areas, etc..; physical quantities are…

A theory in which points, lines, areas and volumes are on on the same footing is investigated. All those geometric objects form a 16-dimensional manifold, called C-space, which generalizes spacetime. In such higher dimensional space…

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…

Clifford algebras are important structures in Geometric Algebra and Quantum Mechanics. They have allowed a formalization of the primitive operators in Quantum Theory. The algebras are built over vector spaces with dimension a power of 2…

We demonstrate the emergence of the conformal group SO(4,2) from the Clifford algebra of spacetime. The latter algebra is a manifold, called Clifford space, which is assumed to be the arena in which physics takes place. A Clifford space…

The mathematical foundations of relativistic quantum mechanics is largely based upon the discovery of the Pauli and Dirac matrices. An algebra which lies at an even more fundamental level is the geometric Clifford algebra with metric…

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…

A generalized Clifford manifold is proposed in which there are coordinates not only for the basis vector generators, but for each element of the Clifford group, including the identity scalar. These new quantities are physically interpreted…

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…

Starting from the geometric calculus based on Clifford algebra, the idea that physical quantities are Clifford aggregates ("polyvectors") is explored. A generalized point particle action ("polyvector action") is proposed. It is shown that…

A solution to the 50 year old problem of a spinning particle in curved space has been recently derived using an extension of Clifford calculus in which each geometric element has its own coordinate. This leads us to propose that all the…

This is an introduction to geometric algebra, an alternative to traditional vector algebra that expands on it in two ways: 1. In addition to scalars and vectors, it defines new objects representing subspaces of any dimension. 2. It defines…

I apply the algebraic framework introduced in arXiv:1101.4542v3[math.MG] to Minkowski (pseudo-Euclidean) spaces in 2, 3, and 4 dimensions. The exposition follows the template established in arXiv:1307.2917[math.MG] for Euclidean spaces. The…

The necessary appearance of Clifford algebras in the quantum description of fermions has prompted us to re-examine the fundamental role played by the quaternion Clifford algebra, C(0,2). This algebra is essentially the geometric 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…

We explore the consequences of space and time described within the Clifford multivector of three dimensions $ Cl_{3,0}$, where space consists of three-vectors and time is described with the three bivectors of this space. When describing the…

In a companion article, the Clifford bundle over spacetime was used as a geometric framework for obtaining coupled Dirac and Einstein equations. Other forces may be incorporated using minimal coupling. Here the fundamental forces that are…

Geometric algebra was initiated by W.K. Clifford over 130 years ago. It unifies all branches of physics, and has found rich applications in robotics, signal processing, ray tracing, virtual reality, computer vision, vector field processing,…