D. Lukman

On the origin of families of quarks and leptons—predictions for four families

The approach unifying all the internal degrees of freedom?proposed by one of us?offers a new way of understanding families of quarks and leptons: a part of the starting Lagrange density in d?(=1+13), which includes two kinds of spin connection fields?the gauge fields of two types of Clifford algebra objects?transforms the right-handed quarks and leptons into left-handed ones manifesting in d=1+3 the Yukawa couplings of the Standard Model. We study the influence of the way of breaking symmetries on the Yukawa couplings and estimate properties of the fourth family?the quark masses and the mixing matrix, investigating the possibility that the fourth family of quarks and leptons appears at low enough energies to be observable with the new generation of accelerators.

Spinor states on a curved infinite disc with non-zero spin-connection fields

In the paper by Lukman et al (2011 New J. Phys. 13 103027), a step towards realistic Kaluza–Klein (like) theories was made by presenting the case of a spinor in d = (1 + 5) compactified on a (formally) infinite disc with the zweibein, which makes a disc curved on an almost S2, and with the spin connection field, which allows such a sphere only one massless spinor state of a particular charge, coupling the spinor chirally to the corresponding Kaluza–Klein gauge field. The solutions for the massless spinor state were found for a range of spin connection fields, as well as the massive ones for a particular choice of the spin connection field. In this paper we present the massless and massive spinor states for the whole range of parameters of the spin connection field that allow only one massless solution.

Massless and massive representations in the spinor technique

The technique for representing spinors and the definition of the discrete symmetries is used to illustrate on a toy model properties of massless and massive spinors states, in the first and the second quantized picture. Since in this toy model the number of the starting massless representations is well-defined as well as the origin of masses and charges in d = (3+1) space, this contribution might help to clarify the problem about Dirac, Weyl and Majorana kinds of representations in physically more interesting cases.