Fuzzy dimensions and Planck$apos$s uncertainty principle for p-branes

Abstract

Abstract. The explicit form of the quantum propagator of a bosonic p-brane, previously obtained by the authors in the quenched-minisuperspace approximation, suggests the possibility of a novel, unified, description of p-branes with different dimensionality. The background metric that emerges in this framework is a quadratic form on a Clifford manifold. Substitution of the Lorentzian metric with the Clifford line element has two far reaching consequences. On the one hand, it changes the very structure of the spacetime fabric since the new metric is built out of a minimum length below which it is impossible to resolve the distance between two points; on the other hand, the introduction of the Clifford line element extends the usual relativity of motion to the case of relative dimensionalism of all p-branes that make up the spacetime manifold near the Planck scale.

A Theory of Quantized Fields Based on Orthogonal and Symplectic Clifford Algebras

“…One possibility [30,31,66] is to replace spacetime with Clifford space [13]- [15], which is a manifold of dimension N = 2 n , whose tangent space at any point X is a Clifford algebra Cl(n). Clifford space is a quenched configuration space associated with p-branes [67,68,66]. One can then proceed as we did in this paper, and arrive at the set of fermionic field operators {h α(X) ,h α(X) }, where α now runs from 1 to 2 N , because we replaced n-dimensional spacetime with Ndimensional Clifford space.…”

An extra structure of spacetime: a space of points, areas and volumes

“…In order to avoid infinite dimensional description of branes, one can introduce a quenched description [15,16] working in a finite dimensional subspace of M-space. The finite dimensional space is the space of oriented r-areas that we associate with closed (r − 1)-branes, or open r-branes.…”

On the Unification of Interactions by Clifford Algebra

“…C-space is a generalization of spacetime, and describes a geometry of oriented r-loops. The latter objects can be considered as being associated with fundamental strings and branes, which are infinite dimensional objects, but can be described within a quenched, minisuperspace description with a finite number of degrees of freedom [14,15]. Since C-space of 4-dimensional spacetime has 16 dimensions, it can incorporate,à la Kaluza-Klein, the 4-dimensional gravity, and other gauge interactions [16]- [19].…”