A Unified Description of Particles, Strings and Branes in Clifford Spaces and p-brane/polyparticle Duality

It is proposed how the Extended Relativity Theory in C-spaces (Clifford spaces) allows a unified formulation of point particles, strings, membranes and p-branes, moving in ordinary target spacetime backgrounds, within the description of a single polyparticle moving in C-spaces. The degrees of freedom of the latter are provided by Clifford polyvector-valued coordinates (antisymmetric tensorial coordinates). A correspondence between the p-brane (p-loop) wave functional “Schroedinger-like” equations of Ansoldi-Aurilia-Spallucci and the polyparticle wave equation in C-spaces is found via the polyparticle/p-brane duality/correspondence. The crux of exploiting this correspondence is that it might provide another unexplored avenue to quantize p-branes (a notoriously difficult and unsolved problem) from the more straightforward quantization of the polyparticle in C-spaces, even in the presence of external interactions. We conclude with some comments about the compositeness nature of the polyvector-valued coordinate operators in terms of ordinary p-brane coordinates via the evaluation of n-ary commutators