Clifford Space as the Arena for Physics

Abstract

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 centre of mass is a point, by generalizing the latter concept, we associate with every extended object a set of $r$-loops, $r=0,1,...,n-1$, enclosing oriented $(r+1)$-dimensional surfaces represented by Clifford numbers called $(r+1)$-vectors or multivectors. Superpositions of multivectors are called polyvectors or Clifford aggregates and they are elements of Clifford algebra. The set of all possible polyvectors forms a manifold, called $C$-space. We assume that the arena in which physics takes place is in fact not Minkowski space, but $C$-space. This has many far reaching physical implications, some of which are discussed in this paper. The most notable is the finding that although we start from the constrained relativity in $C$-space we arrive at the unconstrained Stueckelberg relativistic dynamics in Minkowski space which is a subspace of $C$-space.

30 pages, 4 figures; Talk presented at 3rd Biennial Conference of the International Association for Relativistic Dynamics (IARD), Washington DC, 26-26 June 2002

References in corpus (1)

• Redefining Spinors in Lorentz-Violating QED

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