A chiral theory on a lattice

The author presented the details of a theoretical analysis of a SUL(2) X UR(1) chiral theory with multifermion couplings on a lattice. The existence of a possible scaling region in the phase space of multifermion couplings necessary for defining the continuum limit of chiral fermions is advocated. In this region no spontaneous symmetry breaking occurs; the 'spectator' fermion ψR(x) is a free mode and thus decoupled; doublers decouple as massive Dirac fermions consistently with the SUL(2) X UR(1) chiral symmetry, whereas the normal mode of ψLi(x) is plausibly expected to be chiral in the continuum limit. Such conclusions are not in agreement with the general belief of the definite failure of theories of this kind