Left and right handedness of fermions and bosons

It is shown, by using Grassmann space to describe the internal degrees of freedom of fermions and bosons, that the Weyl like equation exists not only for massless fermions but also for massless gauge bosons. The corresponding states have well defined helicity and handedness. It is shown that spinors and gauge bosons of the same handedness only interact.Comment: 18 pages, LaTeX, no figures, typographical errors corrected and a few sentences added to clarify some issue

The "approach unifying spin and charges" predicts the fourth family and a stable family forming the dark matter clusters

The Approach unifying spin and charges, assuming that all the internal degrees of freedom---the spin, all the charges and the families---originate in $d > (1+3)$ in only two kinds of spins (the Dirac one and the only one existing beside the Dirac one and anticommuting with the Dirac one), is offering a new way in understanding the appearance of the families and the charges (in the case of charges the similarity with the Kaluza-Klein-like theories must be emphasized). A simple starting action in $d >(1+3)$ for gauge fields (the vielbeins and the two kinds of the spin connections) and a spinor (which carries only two kinds of spins and interacts with the corresponding gauge fields) manifests after particular breaks of the starting symmetry the massless four (rather than three) families with the properties as assumed by the Standard model for the three known families, and the additional four massive families. The lowest of these additional four families is stable. A part of the starting action contributes, together with the vielbeins, in the break of the electroweak symmetry manifesting in $d=(1+3)$ the Yukawa couplings (determining the mixing matrices and the masses of the lower four families of fermions and influencing the properties of the higher four families) and the scalar field, which determines the masses of the gauge fields. The fourth family might be seen at the LHC, while the stable fifth family might be what is observed as the dark matter.Comment: 11 pages, to appear in Proceedings to the 5th International Conference on Beyond the Standard Models of Particle Physics, Cosmology and Astrophysics, Cape Town, February 1- 6, 2010

Can the spin-charge-family theory explain baryon number non conservation?

The spin-charge-family theory, in which spinors carry besides the Dirac spin also the second kind of the Clifford object, no charges, is a kind of the Kaluza-Klein theories. The Dirac spinors of one Weyl representation in $d=(13+1)$ manifest in $d=(3+1)$ at low energies all the properties of quarks and leptons assumed by the standard model. The second kind of spins explains the origin of families. Spinors interact with the vielbeins and the two kinds of the spin connection fields, the gauge fields of the two kinds of the Clifford objects, which manifest in $d=(3+1)$ besides the gravity and the known gauge vector fields also several scalar gauge fields. Scalars with the space index $s\in (7,8)$ carry the weak charge and the hyper charge ($\mp \frac{1}{2}, \pm \frac{1}{2}$, respectively), explaining the origin of the Higgs and the Yukawa couplings. It is demonstrated in this paper that the scalar fields with the space index $t\in (9,10,\dots,14)$ carry the triplet colour charges, causing transitions of antileptons and antiquarks into quarks and back, enabling the appearance and the decay of baryons. These scalar fields are offering in the presence of the right handed neutrino condensate, which breaks the ${\cal C}{\cal P}$ symmetry, the answer to the question about the matter-antimatter asymmetry.Comment: 48 pages, in press in Phys. Rev. D, modified version of the talk in the Proceedings to the $17^th$ Workshop "What comes beyond the standard models", Bled, 20-28 of July, 201