Carlos Castro, Center for Theoretical Studies of Physical Systems, Clark Atlanta University, Atlanta, GA. 30314; email@example.com, December, 2014. Submitted to Phys. Letts. B.
Abstract: 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.
Keywords : Cliord algebras; Extended Relativity in Cliord Spaces; Strings; Branes; M-theory; polyparticle/p-brane duality; loop wave functional equations; Born-Dirac oscillator; n-ary commutators.
Source: Email from C. Castro, perelmanc_AT_hotmail.com, 2015/01/05 11:56