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By quantizing a realistic field theory in one space and one time dimension at equal light-cone time T = 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.

Tin 1 QCD light cone lUmiltonian is diagcmalized in adisrrete momentum spare baMs. Hit-spectra and w^wfunrtiuns for various coupling constants, numbers of color, arid baryon numb«-r are computed. Talk Presented to the Ohio Slate Workshop OnRflAiivistic A/amBody Physics, Columbus, Ohio, June 6 9J98H•

In the preceding paper, the field-theoretic bound-state problem in 1 + 1 dimensions was mapped to the problem of diagonalizing a strictly finite-dimensional Hamiltonian matrix by quantizing at equal light-cone time. In this paper, we calculate the invariant mass spectrum for the Yukawa theory $4111. The spectrum is shown to be independent of the momentum cutoff in the limit A-+CC and more complex with increasing harmonic resolution K. The results are compared with the recent work of Brooks and Frautschi, who apply conventional space-time quantization. Because of incompatible cutoffs, we reproduce their results only qualitatively, for a rather small value of A. We propose an explanation for their nonunique mass renormalization. We also discuss the straightforward application of the discretieed light-cone quantization to non-Abelian field theories in 1 + 1 dimensions, and the generalization to 3 + 1 dimensions.

Abstract:The averaging procedure an Strutlnsky's method of shell correctmns is formulated for a general type of averaging functmn. In the case of the harmomc-oscfllator potentml, the method is proved analytically to gave the same results as semlclasslcal methods. For the mfimterectangular-box potentml, an uncertamty in the value of the shell correction 6U of up to ,~ 0.5 MeV ts shown to extst, the sem~classxcal value lying wRhm these hm~ts. In using reahstlc finite-depth potentmls, no restrictions need to be made on the vahdlty of Strutmsky's method, and the uncertainty m the values of 6U as estimated to be less than ~ 0 5 MeV.

The method of discretized light-cone quantization (DLCQ), recently proposed for obtaining nonperturbative solutions to field theories, is applied to quantum electrodynamics in one space dimension (QEDq). The spectrum of invariant masses and the eigenfunctions of the light-cone Hamiltonian are calculated; i.e. , the bound-state problem is solved for all values of the coupling constant. For very strong coupling (Schwinger model proper) DLCQ reproduces one to one the known exact solutions. For nonvanishing fermion mass (massive Schwinger model) the results of DLCQ agree with earlier work and in particular with a lattice gauge calculation.

We propose a model for generalized parton distributions of the pion based on the power-law Ansatz for the effective light-cone wave function