Pauli-villars Regularization and Discrete Light-cone Quantization in Yukawa Theory

As a step toward development of a method for nonperturbative solution of fourdimensional quantum field theories, we consider a single-fermion truncation of Yukawa theory in discrete light-cone quantization (DLCQ). 1 To regulate the theory we introduce Pauli-Villars (PV) bosons with indefinite metric 2 into the Fock basis. This extends earlier work on model theories by Brodsky, Hiller and McCartor 3,4 to a more physical situation. The importance of Pauli–Villars regularization stems from its ability to regulate the continuum theory with counterterms generated automatically, except for a trivial mass counterterm. The numerical method, in this case DLCQ, can then be applied to a finite theory. The bare parameters are fixed via physical constraints and become functions of the PV masses and of any numerical parameters. The original theory is recovered in the following sequence of limits: infinite numerical resolution, infinite (momentum) volume, and infinite PV masses. The DLCQ formulation is based on periodic boundary conditions for bosons and antiperiodic conditions for fermions in a light-cone box −L < x− ≡ (t − z) < L, −L⊥ < x, y < L⊥. The light-cone 3-momentum p ≡ (p, ~p⊥) is then on a discrete grid specified by integers n = (n, nx, ny): p + ≡ (E + pz) = π Ln, ~ p⊥ = ( π L⊥ nx, π L⊥ ny). The limit L → ∞ can be exchanged for a limit in terms To appear in the proceedings of the CSSM Workshop on Light-Cone QCD and Nonperturbative Hadron Physics, Adelaide, Australia, December 13-21, 1999. Work supported in part by the Department of Energy, contract DE-FG02-98ER41087.