Hints of a New Relativity Principle from p-brane Quantum Mechanics

This report is an extension of previous one hep-th/9812189. Several quantum mechanical wave equations for p-branes are proposed. The most relevant p-brane quantum mechanical wave equations determine the quantum dynamics involving the creation/destruction of p-dimensional loops of topology S^p, moving in a D dimensional spacetime background, in the quantum state $\Phi$. To implement full covariance we are forced to enlarge the ordinary Relativity principle to a new Relativity principle, suggested earlier by the author based on the construction of {\bf C}-space, and also by Pezagglia's Polydimensional Relativity, where all dimensions and signatures of spacetime should be included on the same footing.