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

TL;DR

This paper proposes new quantum mechanical wave equations for $p$-branes, suggesting an extension of Einstein's relativity to include all dimensions and signatures on equal footing, based on the concept of C-space.

Contribution

It introduces a novel set of $p$-brane quantum wave equations and advocates for a new relativity principle that unifies all spacetime dimensions and signatures.

Findings

Quantum $p$-brane wave equations are formulated.

A new relativity principle based on C-space is proposed.

Implications for unifying spacetime dimensions are discussed.

Abstract

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 Pezzaglia's Polydimensional Relativity, where all dimensions and signatures of spacetime should be included on the same footing.