Norma Susana Mankoc Borstnik

Unification of Spins and Charges

Polynomials in Grassmann algebra can be used to describe the internal degrees, spins and charges of spinors, scalars, and vectors. It was shown by Mankoc Borstnik and Nielsen that Kahler spinors can be generalized to describe spins of vectors as well as spins and charges of scalars, vectors, and spinors. In dimensions 14 and higher, the spontaneous breaking of symmetry leads gravity in d dimensions to manifest in 4-dimensional subspace as ordinary gravity and all needed gauge fields as well as the Yukawa couplings. Both approaches, Kahlers one (if generalized) and ours, manifest four generations of massless fermions, which are left-handed SU(2) doublets and right-handed SU(2) singlets. A possible way of spontaneously breaking symmetries is pointed out at the level of canonical momentum.Polynomials in Grassmann algebra can be used to describe the internal degrees, spins and charges of spinors, scalars, and vectors. It was shown by Mankoč Borštnik and Nielsen that Kähler spinors can be generalized to describe spins of vectors as well as spins and charges of scalars, vectors, and spinors. In dimensions 14 and higher, the spontaneous breaking of symmetry leads gravity in d dimensions to manifest in 4-dimensional subspace as ordinary gravity and all needed gauge fields as well as the Yukawa couplings. Both approaches, Kählers one (if generalized) and ours, manifest four generations of massless fermions, which are left-handed SU(2) doublets and right-handed SU(2) singlets. A possible way of spontaneously breaking symmetries is pointed out at the level of canonical momentum.

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 vector bosons. The corresponding states have well defined helicity and handedness. It is also shown that spinors and vector bosons interact only if both are of the same handedness.

IS THE FIFTH FAMILY PREDICTED BY THE "APPROACH UNIFYING SPIN AND CHARGES" WHAT FORMS THE DARK MATTER?

Norma Susana Mankoc Borstnik a Faculty of Mathematics and Physics, University of Ljubljana, 1000 Ljubljana, Slovenia Abstract.The approach unifying spin and charges [1–4], which predicts that all the internal degrees of freedom—the spin, all the charges and the families—originate in only two kinds of spins in d > (1 + 3), offers a new way to understanding the appearance of the charges and the families. A simple starting Lagrange density for gauge fields and for spinors in d > (1 + 3), which carry nothing but two kinds of spins—the Dirac one and the additional one anticommuting with the Dirac one—and interact with only the gravitational field through the vielbeins and the two kinds of the spin connection fields (the gauge fields of the two kinds of the Clifford algebra objects) manifests (after particular breaks of the starting symmetry) in d = (1 + 3) the properties of fermions and bosons as postulated by the standard model of the electroweak and colour interactions, with the Yukawa couplings included. The approach predicts the fourth family with the masses to be possibly seen at the LHC or at somewhat higher energies and the fifth family, which decouples in the Yukawa couplings from the lower four families. The properties of this fifth family members through the evolution of the universe up to today are estimated, predicting that they are what the dark matter is made out of.