2001/05/13 by Yu. F. Pirogov, Pirogov, Yu. F.
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Cosmology and Gravitation Theories #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Phenomenology (hep-ph) #Relativity and Gravitational Theory #gr-qc #hep-ph
paper · pdf · doi:10.48550/arxiv.hep-ph/0105112
10 pages, LaTeX. Report presented at the XI-th Int. School "Particles and Cosmology", Baksan Valley, 18-24 April, 2001
arxiv created 2001/05/13 · openalex publication_date 2001/05/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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≥4, the complex symplectic ones Sp(2l,C), l≥1 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=4l2 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.