FIZIKA B 8 (1999) 2, 407-418

UNIFICATION OF SPINS AND CHARGES UNIFIES ALL INTERACTIONS

NORMA MANKOČ BORŠTNIK

Department of Physics, University of Ljubljana, Jadranska 19
and J. Stefan Institute, Jamova 39, Ljubljana, 1 111, Slovenia

Received 28 January 1999; Accepted 19 July 1999

In a space of d Grassmann coordinates, two types of generators of Lorentz transformations, one of spinorial and the other of vectorial character, define the representations of the group SO(1,d-1) for fermions and bosons, respectively. The eigenvalues of commuting operators of the subgroups SO(1,3), SU(3), SU(2) and U(1) can be identified with spins and Yang-Mills charges of either fermionic or bosonic fields, which allows the unification of all the internal degrees of freedom, separately for fermions and separately for bosons. When, accordingly, all interactions are unified, the Yang-Mills fields, the Higgs fields and the Yukawa couplings appear as a part of a gravitational field. The theory suggests four families of quarks and leptons. The equal number of fermions and bosons assures supersymmetry.

PACS numbers: 12.10.Kt, 12.90.+b
UDC 539.126

Keywords: Grassmann coordinates, generators of Lorentz transformations, spinorial and vectorial representations of group SO(1,d-1) for fermions and bosons, eigenvalues of commuting operators, subgroups SO(1,3), SU(3), SU(2) and U(1), spins and Yang-Mills charges, fermionic or bosonic fields, unification of all the internal degrees of freedom, unification of interactions, Yang-Mills fields, Higgs fields, Yukawa couplings, gravitational field, four families of quarks and leptons, supersymmetry

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