For unified description of fundamental fermions, a theory of multi-spinor fields is formulated on an algebra which consists of triple-tensor-products of elements of the Dirac algebra. Chiral combinations of multi-spinor fields form reducible representations of the Lorentz group possessing component fields with spin 1/2, which can be interpreted as expressing three ordinary families and an additional fourth family of quarks and leptons. Apart from the gauge and Higgs fields of the standard model which interact with the fermions of the three families, we assume the existence of extra gauge and Higgs fields which interact exclusively with the fermions of the fourth family. While the fields of the standard model organize the bright world including baryonic matter, the fields related with the fourth family are considered to characterize a dark world which can accommodate dark matter. Scenarios for appearance of dark matter and relations between the bright and dark worlds are discussed.

NOTES

(NOTE UNSUSUAL DATE)