Solving field theory in one space and one time dimension

Abstract

By quantizing a realistic field theory in one space and one time dimension at equal light-cone time τ=t+x/c rather than at equal time t, one can find exact solutions to the bound-state problem. The method is nonperturbative and amounts to the diagonalization of finite matrices in Fock space. It applies also for non-Abelian gauge theory in 1+1 dimensions, but is demonstrated here for the simple case of fermions interacting with scalar fields. The success of the light-cone quantization method rests on the existence of a new dynamical quantum number, the harmonic resolution K, which can be understood as the ratio of a characteristic length, the box size L, and the Compton wavelength of a massive particle. We emphasize the appearance of self-induced instantaneous inertias.