Fuzzy dimensions and Planck's Uncertainty Principle for p-branes

TL;DR

This paper explores a novel framework for p-branes using Clifford manifolds, revealing a minimum length scale and a new form of relativity that extends to the dimensionality of branes near the Planck scale.

Contribution

It introduces a Clifford manifold-based approach to p-branes, unifying different dimensions and incorporating a minimum length and relative dimensionalism at quantum gravity scales.

Findings

Discovery of a quadratic form on a Clifford manifold for p-brane propagators.

Introduction of a minimum length scale below which distances cannot be resolved.

Extension of relativity to include relative dimensionalism of p-branes.

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.