A unified description of particles, strings and branes in Clifford spaces and p-brane/polyparticle duality

It is described 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) "Schr�dinger-like" equations of Ansoldi-Aurilia-Spallucci and the polyparticle wave equation in C-spaces is found via the polyparticle/p-brane correspondence. This correspondence 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 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. © 2016 World Scientific Publishing Company.

• Main Author: Castro, C. (author)
• Format: article
• Published: 2016
• Subjects: Born-Dirac oscillator; branes; Clifford algebras; Extended Relativity in Clifford spaces; M-theory; n-ary commutators; Nambu bracket; polyparticle/p-brane duality; strings
• Online Access: http://10.1142/S0219887815501339; http://dspace.utpl.edu.ec/handle/123456789/18904