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 ψ¯φψ. The spectrum is shown to be independent of the momentum cutoff in the limit Λ-->∞ 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 Λ. 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.
- Publication:
-
Physical Review D
- Pub Date:
- October 1985
- DOI:
- 10.1103/PhysRevD.32.2001
- Bibcode:
- 1985PhRvD..32.2001P
- Keywords:
-
- 11.10.Ef;
- 03.70.+k;
- 11.10.St;
- 11.15.Tk;
- Lagrangian and Hamiltonian approach;
- Theory of quantized fields;
- Bound and unstable states;
- Bethe-Salpeter equations;
- Other nonperturbative techniques