Heuristic derivation of Weinberg’s angle from space-time and gauge symmetries unification

Besprosvany, J.
August 2000
AIP Conference Proceedings;2000, Vol. 531 Issue 1, p289
Academic Journal
We analyze modern theories' use of the concepts of the wave function, the field, and the underlying space-time in which they live, at the local and global levels and point out at incompatibilities involved. These are resolved by proposing a description in which these three items are considered inseparable. We implement this idea by assigning group generators to Lorentz scalars in an extended Clifford algebra. In the simplest application of the theory, we associate the vector carriers of the SU(2)[sub L] × U(1) isospin and the hypercharge symmetries with linear combinations of elements in the Clifford algebra which reproduce the required quantum number of leptons in the interactions. We show that at symmetry breaking to an electromagnetic U(1), the demand of the presence of a non-axial vector, to be linked to the electromagnetic field, leads to a Weinberg's angle θ[sub W] with sin²(θ[sub W]) = .25.


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