-SLAC - PUB - 3701 June 1985 CT) Solving Field Theory in One-Space-One-Time Dimension* HANS- CHRISTIAN PAULI+ and STANLEY J. BRODSKY Stanford Linear Accelerator Center Stanford University, Stanford, California, 94305 ABSTRACT By quantizing a realistic field theory in one space and one time dimension at equal light cone time r = t + x/c rather than at equal time t, one can find exact solutions to the bound state problem. The method is non-perturbative 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 wave length of a massive particle. We emphasize the appearance of self-induced instantaneous inertias. - Submitted to Physical Review D * Work supported by the Department of Energy, contract DE - AC03 - 76SF00515. + On leave from Max-Planck-Institut fiir Kernphysik, Heidelberg, Germany