Space-time symplectic extension

Abstract

It is conjectured that in the origin of space-time there lies a symplectic rather than metric structure. The complex symplectic symmetry Sp(2l,C), l\ge1 instead of the pseudo-orthogonal one SO(1,d-1), d\ge4 is proposed as the space-time local structure group. A discrete sequence of the metric space-times of the fixed dimensionalities d=(2l)^2 and signatures, with l(2l-1) time-like and l(2l+1) space-like directions, defined over the set of the Hermitian second-rank spin-tensors is considered as an alternative to the pseudo-Euclidean extra dimensional space-times. The basic concepts of the symplectic framework are developed in general, and the ordinary and next-to-ordinary space-time cases with l=1,2, respectively, are elaborated in more detail. In particular, the scheme provides the rationale for the four-dimensionality and 1+3 signature of the ordinary space-time.