The Generative Process of Space-Time and Strong Interaction Quantum Numbers of Orientation

Abstract

An image of physical fields is posed to the reader that does no longer rely on a pregiven concept of spacetime and coordinate systems respectively, wherein equations of motion are formulated a posteriori. But a view is offered where well known properties of spacetime and fields are outcomes of one and the same generative process or grammar. This approach is based theoretically on Clifford algebras and practically supported by the computer algebra system of CLICAL. For instance, it is not postulated that the orientation of space is a priori determined, but that it is the outcome or a process and therefore subject to uncertainty as any quantum field in physical spacetime. Making use of the Clifford algebra Cℓ_3,1, basic spin representations of the octahedral space group are O _h constructed. Next it can be shown that the quarks can be conceived as quantum states of the central symmetry operators and well known Schönfließ symbols ₁ C ₂, ₂ C ₂, ₃ C ₂ of O _h with the eigenvalues +1 or −1. Thus the quarks turn out to represent quantized states of orientation which may be the reason why they are confined. Next the algebraic relations between the orientation symmetry V _h and the Gell-Mann matrices are established and finally the Gell-Mann-Nishijima relation is derived from geometry. In this way an inner symmetry is linked to an outer symmetry. Orientation numbers can be defined as parties of oriented plane areas e_i,j. Their values are calculated for the case of baryon octet of the nucleons and the quarks. This example makes it clear why quarks are the only particles with orientation quantum numbers ±1.