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IHEP 2001 - 19 (in Russian) | |
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| Yu.F. Pirogov | ||
| Space-time symplectic extension | ||
| Protvino, 2001.- p.11, refs.:9. | ||
It is conjectured that in the origin of \st there lies a symplectic rather than metric structure. The complex symplectic symmetry $Sp(2l,C)$, $l\ge 1$ instead of the pseudo-orthogonal one $SO(1,d-1)$, $d\geq 4$ 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 \st 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.
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