Two-boson truncation of Pauli-Villars-regulated Yukawa theory

Stanley J. Brodsky, John R. Hiller, Gary McCartor

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We apply light-front quantization, Pauli-Villars regularization, and numerical techniques to the nonperturbative solution of the dressed-fermion problem in Yukawa theory in 3 + 1 dimensions. The solution is developed as a Fock-state expansion truncated to include at most one fermion and two bosons. The basis includes a negative-metric heavy boson and a negative-metric heavy fermion to provide the necessary cancellations of ultraviolet divergences. The integral equations for the Fock-state wave functions are solved by reducing them to effective one-boson-one-fermion equations for eigenstates with Jz = 1/2. The equations are converted to a matrix equation with a specially tuned quadrature scheme, and the lowest mass state is obtained by diagonalization. Various properties of the dressed-fermion state are then computed from the nonperturbative light-front wave functions. This work is a major step in our development of Pauli-Villars regularization for the nonperturbative solution of four-dimensional field theories and represents a significant advance in the numerical accuracy of such solutions.

Original languageEnglish (US)
Pages (from-to)1240-1264
Number of pages25
JournalAnnals of Physics
Issue number5
StatePublished - May 2006

Bibliographical note

Funding Information:
This work is supported in part by the Department of Energy under Contract Nos. DE-AC02-76SF00515, DE-FG02-98ER41087, and DE-FG03-95ER40908.

Funding Information:
This work was supported by the Department of Energy through Contracts DE-AC02-76SF00515 (S.J.B.), DE-FG02-98ER41087 (J.R.H.), and DE-FG03-95ER40908 (G.M.), and by the Minnesota Supercomputing Institute through grants of computing time.


  • Light-cone quantization
  • Pauli-Villars regularization
  • Yukawa theory


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