Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory

Brodsky, Stanley J. ; /SLAC ; Hiller, John R. ; /Minnesota U., Duluth ; McCartor, Gary ; U., /Southern Methodist

Stanford Linear Accelerator Center

关键词: Ultraviolet Divergences;    Integral Equations;    Dimensions;    Field Theories;    Quantization;   

DOI  :  10.2172/878438
RP-ID  :  SLAC-PUB-11400
RP-ID  :  AC02-76SF00515
RP-ID  :  878438

美国|英语

来源: UNT Digital Library

【 摘 要 】

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 in order 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 J{sub z} = 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.