The four electroweak generators of the SM local

gauge group SU[(2).

Let G be a topological group, let X be a space, and let P [right arrow] X be a principal G-bundle with gauge group G(P).

k] be the gauge group of the principal G-bundle [P.

Firstly, for Auyang the gauge group is interpreted passively.

that the gauge group relates not just representations of events but events themselves.

finite) binary rotational subgroups of the EW

gauge group SU[(2).

Other subjects explored are topological field theories with non-semisimple

gauge group of symmetry, continuity equations in Riemannian spaces, the non-Hamiltonian nature of nucleon dynamics in an effective field theory, and singular value decomposition and Lanczos potential.

Herein I determine the true source of the PMNS matrix elements by using the linear superposition of the generators for 3 discrete binary rotational subgroups of the Standard Model (SM) electroweak

gauge group SU[(2).

These seven subgroups of the SM local

gauge group act in the [R.

SM does not clarify the origin of its

gauge group SU(3)xSU(2)xU(1) and why quarks and lepton occur as representations of this group;

If lepton and quark states represent specific finite binary rotational subgroups of the SM

gauge group, unification with gravitation is accomplished by combining finite subgroups of the Lorentz group SO(3,1) with the specific finite SM subgroups.

Eight chapters address notations and conventions, calculational techniques in field theory and the status of quantum dynamics, global and local symmetries and the construction of non-abelian gauge theories, the strong interactions and the structure and tests of quantum chromodynamics, electroweak interactions and theory (including neutrino masses), extensions to the standard model, supersymmetry, extended

gauge groups, and grand unification.