Author name Giuliano Bettini Title

As I showed in my previous writings (“Electroweak Forces Acting on TE, TM, TEM”), a field similar to the gauge boson W provides a helical motion that transforms a TEM in a TE (or TM) in a waveguide. This helical motion in the Hestenes interpretation of electron is the zitterbewegung. In “Electroweak Forces Acting on TE, TM, TEM” I just talk about electromagnetic fields, TEM and TE, TM. Similarities inevitable appear, all questionable, with neutrinos and electrons / positrons. However Hestenes in "Spacetime calculus”, speaking of the helical motion ie zitterbewegung makes more explicitly this hypothesis: "This opens up possibilities for integrating the zitterbewegung idea with electroweak theory. Evidently that would obviate the need for including Higgs bosons in the theory, since the zitterbewegung provides an alternative mechanism to account for the electron mass." In face of a possible elimination of the Higgs particle from the electroweak theory it appears useful to repeat my ideas in a popular way. Zitterbewegung and Higgs particle. A short introduction. 1 Introduction and summary I showed in my previous writings [16] that a field similar to the gauge boson W provides in a TEM a helical motion that transforms the TEM in a TE (or TM) in waveguide. This helical motion, in the Hestenes interpretation of the electron, is the zitterbewegung. In [16] I just talk about electromagnetic fields, TEM and TE, TM. I noticed that a TEM is wrapped in a waveguide and becomes a TE or TM with mass and.... the Higgs particle do not appear. Similarities inevitable appear, already appeared in [15], all questionable, with neutrinos and electrons / positrons. Hestenes however in Spacetime calculus, speaking of the helical motion ie zitterbewegung, makes a more explicit hypothesis that, given the similarities, it seems interesting: "This opens up possibilities for integrating the zitterbewegung idea with electroweak theory. Evidently that would obviate the need for including Higgs bosons in the theory, since the zitterbewegung provides an alternative mechanism to account for the electron mass." In the face of a possible elimination of the Higgs particle from the electroweak theory it appears useful to repeat my ideas in a popular way. Why we can and should speak of the electroweak force on TE, TM and TEM is extensively treated in [16], from which I also report here the references [1]...[15], but in short: 1°) the group that leaves unchanged the electromagnetic field energy momentum vector is not only the electromagnetic gauge group φ ψ ψ ψ i e = → ' (Hestenes) but the group ( ) ( ) 1 2 U SU ⊗ ; 2°) the application of a gauge transformation ( ) ( ) 1 2 U SU ⊗ in an abstract space is the way we produce and describes the unification of the electromagnetic forces and the electroweak forces. It is obvious that should be able to see the effect of a ( ) ( ) 1 2 U SU ⊗ transformation even on the electromagnetic field. In addition, I say, not in an abstract space but in the true space. This effect should manifest itself (and manifested) as electroweak force on the TE TM TEM fields as I showed in [16]. The exposition we're doing here is deliberately simple and (almost) without formulas. First: go down again the geometric effect of the generators of the group ( ) ( ) 1 2 U SU ⊗ . Second: I show how geometrically and intuitively operate on the fields TE, TM and TEM physical objects similar to the W and Z°, and to the photon γ . In particular in section 2 examines the first question: there are electroweak force acting on TE, TM and TEM fields? I try to give to this question an answer not mathematics but qualitative. I highlight objects that act on TE, TM and TEM producing effects similar to the action of the particles W and Z°, and γ . Then I try to translate the action of these objects in these mathematical operators to operate in a similar manner to the Z°, W and γ particles in quantum mechanics. To this end, in Section 3 I briefly summarize the Clifford algebra so far as is necessary. In Section 4 briefly recall the way in which the Clifford algebra and the generators of the group ( ) ( ) 1 2 U SU ⊗ are involved in gauge theories. In Section 5 discusses the geometric action of generators, namely the effect that they have in ordinary space and how it manifests itself. With this background in section 6 discusses the gauge fields attributable to W and γ particles, and interprets the action on electromagnetic fields TE / TM. I note that in particular the action of W result in a mechanism to give mass which is an alternative to the Higgs boson. For completeness of exposition in section 7 discusses the gauge fields attributable to the particle Z° and interprets the action on electromagnetic fields TEM. In the concluding section 8 discusses the reason why these events, taken together, can lead to believe a mathematical theory of electroweak interactions without the intervention of the Higgs boson. 2 – The weak interactions The first problem is: there are forces electroweak fields TE, TM and TEM? I tried to answer with mathematics in [16]. What is not mathematics, but instead a qualitative answer? Particles W and Z° carriers of the weak force should find their interpretation in the action of a radar target from which scattering takes place, or an obstacle in waveguide, or similar. You can view the action of an object on an incident electromagnetic signal to end up saying: “look, this is the action of the Z° particle" or " this is like the action of the W particle "? In [15] have established the similarities I remember here and help me with the drawings. neutrino: TEM circular polarization velocity c electron (and positron): helical e. m. field (TE o TM) circular polarization velocity V We begin to summarize the action of the photon. It changes speed or diverts electrons