2T Physics, Scale Invariance and Topological Vector Fields
arXiv:0706.0532 · doi:10.1007/s10773-007-9598-5
Abstract
We construct, in classical two-time physics, the necessary structure for the most general configuration space formulation of quantum mechanics containing gravity in d+2 dimensions. This structure is composed of a symmetric Riemannian metric tensor and of a vector field that defines a section of a flat U(1) bundle over space-time. This construction is possible because of the existence of a finite local scale invariance of the Hamiltonian and because two-time physics contains, at the classical level, a local generalization of the discrete duality symmetry between position and momentum that underlies the structure of quantum mechanics.
Accepted for publication in International Journal of Theoretical Physics