Discretized light-cone quantization: Solution to a field theory in one space and one time dimension

Abstract

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 \ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\varphi}\ensuremath{\psi}. The spectrum is shown to be independent of the momentum cutoff in the limit \ensuremath{\Lambda}\ensuremath{\rightarrow}\ensuremath{\infty} 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 \ensuremath{\Lambda}. We propose an explanation for their nonunique mass renormalization. We also discuss the straightforward application of the discretized light-cone quantization to non-Abelian field theories in 1+1 dimensions, and the generalization to 3+1 dimensions.