Clifford Space as a Generalization of Spacetime: Prospects for Unification in Physics

Abstract

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 only of points, but also of 1-loops, 2-loops, etc.. They are associated with multivectors which are the wedge product of the basis vectors, the generators of Clifford algebra. We assume that $C$-space is the true space in which physics takes place and that physical quantities are Clifford algebra valued objects, namely, superpositions of multivectors, called Clifford aggregates or polyvectors. We explore some very promising features of physics in Clifford space, in particular those related to a consistent construction of string theory and quantum field theory.

arXiv comment12 pages; Talk presented at {\it 4th Vigier Symposium: The Search For Unity in Physics}, September 15th--19th, 2003, Paris, France

References in corpus (3)

• Higher Derivative Gravity and Torsion from the Geometry of C-spaces
• Pseudo Euclidean-Signature Harmonic Oscillator, Quantum Field Theory and Vanishing Cosmological Constant
• Clifford Algebra Based Polydimensional Relativity and Relativistic Dynamics

Cited by in corpus (6)

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• On a Unified Theory of Generalized Branes Coupled to Gauge Fields, Including the Gravitational and Kalb-Ramond Fields
• An Extra Structure of Spacetime: A Space of Points, Areas and Volumes
• Pati-Salam model in curved space-time from square root Lorentz manifold
• On an Alternative Approach to the Relation between Bosons and Fermions: Employing Clifford Space