Hints of a new relativity principle from p-brane quantum mechanics

This report is an extension of a previous one hep-th/9812189. Several quant um mechanical wave equations for p-branes are pro posed. The most relevant p-brane quantum mechanical wave equations determine the quantum dynamics in volving the creation/destruction of p-dimensional loops of topology S-P, mo ving 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 ba sed on the construction of C-space, and also by Pezzaglia's poly-dimensiona l relativity, where all dimensions and signatures of spacetime should be in cluded on the same footing. (C) 2000 Elsevier Science Ltd. All rights reser ved.