Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory

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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 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 ... continued below

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32 pages

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Brodsky, Stanley J.; /SLAC; Hiller, John R.; /Minnesota U., Duluth; McCartor, Gary & U., /Southern Methodist September 1, 2005.

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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 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.

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32 pages

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  • Report No.: SLAC-PUB-11400
  • Grant Number: AC02-76SF00515
  • DOI: 10.2172/878438 | External Link
  • Office of Scientific & Technical Information Report Number: 878438
  • Archival Resource Key: ark:/67531/metadc879311

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  • September 1, 2005

Added to The UNT Digital Library

  • Sept. 21, 2016, 2:29 a.m.

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  • Dec. 9, 2016, 12:02 a.m.

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Brodsky, Stanley J.; /SLAC; Hiller, John R.; /Minnesota U., Duluth; McCartor, Gary & U., /Southern Methodist. Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory, report, September 1, 2005; [Menlo Park, California]. (digital.library.unt.edu/ark:/67531/metadc879311/: accessed October 19, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.