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

Gauge fields with respect to d=(3+1)d=(3+1) in the Kaluza-Klein theories and in the spin-charge-family theory

It is shown that in the spin-charge-family theory, as well as in all the Kaluza-Klein like theories, vielbeins and spin connections manifest in $d=(3+1)$ space equivalent vector gauge fields, when space with $d\ge5$ manifests large enough symmetry. The authors demonstrate this equivalence in spaces with the symmetry of the metric tensor in the space out of $d=(3+1)$ - $g^{\sigma \tau} = \eta^{\sigma \tau} \,f^{2}$ - for any scalar function $f$ of the coordinates $x^{\sigma}$, where $x^{\sigma}$ denotes coordinates of space out of $d=(3+1)$. Also the connection between vielbeins and scalar gauge fields in $d=(3+1)$ (offering the explanation for the Higgs's scalar) is discussed.Comment: 9 pages, EPJC macros, revised version to be published at EPJ