Symplectic vs pseudo-Euclidean space-time with extra dimensions

Abstract

It is conjectured that the symplectic structure of space-time is superior to the metric one. Instead of the commonly adopted pseudo-orthogonal groups SO(1,d-1), d\ge4, the complex symplectic ones Sp(2l,C), l\ge1 are proposed as the local structure groups of the extended space-time. A discrete series of the metric space-times of the particular dimensionalities d=4l^2 and signatures, with l(2l-1) time and l(2l+1) spatial directions, defined over the set of the Hermitian second-rank spin-tensors is proposed as an alternative to the pseudo-Euclidean space-times with extra dimensions. The one-dimensional time-like direction remaining invariant under fixed boosts makes it possible the non-relativistic causality description despite the presence of extra times.