The Takabayasi Moving Frame, from the a Potential to the Z Boson

Abstract

During the years 1950, an important part of the works of the physicists of the “Louis de Broglie’s school” (in particular O. Costa de Beauregard[1], F. Halbwachs [2], G. Jakobi, G. Lochak [3], T. Takabayasi [4], J.P. Vigier [5]) has been devoted to an intrinsic presentation of the electron Dirac theory. In this presentation, the ab]|a|Abstract formalism of the Dirac spinors was replaced by the use of quantities and equations independant of all galilean frame of the Minkowski spacetime M = R ^{1, 3} (here R ^{p, n-p} means the signature of a R ⁿ euclidean space). So was introduced, in particular, the “Takabayasi frame” which is a frame of four orthonormal spacetime vectors v, n ₁, n ₂, n ₃, defined at each poin x of M, in such a way that v is a timelike vector, the spacetime velocity of the Dirac particle (colinear to the spacetime current j = ρv where ρ > 0 is the probability density), and that the bivector (antisymmetric tensor of rank 2) (hc/2)n ₁ A n ₂ represents the intrinsic angular momentum, or spin.