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Title: Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory

Abstract

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.

Authors:
; ; ; ; ;
Publication Date:
Research Org.:
Stanford Linear Accelerator Center (SLAC)
Sponsoring Org.:
USDOE
OSTI Identifier:
878438
Report Number(s):
SLAC-PUB-11400
hep-ph/0508295; TRN: US0602380
DOE Contract Number:
AC02-76SF00515
Resource Type:
Technical Report
Country of Publication:
United States
Language:
English
Subject:
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ACCURACY; BOSONS; DIMENSIONS; EIGENSTATES; FERMIONS; FIELD THEORIES; INTEGRAL EQUATIONS; QUADRATURES; QUANTIZATION; ULTRAVIOLET DIVERGENCES; WAVE FUNCTIONS; Phenomenology-HEP,HEPTH

Citation Formats

Brodsky, Stanley J., /SLAC, Hiller, John R., /Minnesota U., Duluth, McCartor, Gary, and /Southern Methodist U. Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory. United States: N. p., 2005. Web. doi:10.2172/878438.
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Brodsky, Stanley J., /SLAC, Hiller, John R., /Minnesota U., Duluth, McCartor, Gary, & /Southern Methodist U. Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory. United States. doi:10.2172/878438.
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Brodsky, Stanley J., /SLAC, Hiller, John R., /Minnesota U., Duluth, McCartor, Gary, and /Southern Methodist U. Thu . "Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory". United States. doi:10.2172/878438. https://www.osti.gov/servlets/purl/878438.
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@article{osti_878438,
title = {Two-Boson Truncation of Pauli-Villars-RegulatedYukawa Theory},
author = {Brodsky, Stanley J. and /SLAC and Hiller, John R. and /Minnesota U., Duluth and McCartor, Gary and /Southern Methodist U.},
abstractNote = {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.},
doi = {10.2172/878438},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Thu Sep 01 00:00:00 EDT 2005},
month = {Thu Sep 01 00:00:00 EDT 2005}
}
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DOI:  10.2172/878438
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  • We obtain analytic nonperturbative approximate solutions of Yukawa theory in the one-fermion sector using light-front quantization. The theory is regulated in the ultraviolet by the introduction of heavy Pauli-Villars scalar and fermion fields each with negative norm. In order to obtain a directly soluble problem fermion-pair creation and annihilation are neglected and the number of bosonic constituents is limited to one of either type. We discuss some of the features of the wave function of the eigensolution including its endpoint behavior and spin and orbital angular momentum content. The limit of infinite Pauli-Villars mass receives special scrutiny.

  • ; ; - Annals of Physics (New York)
    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 J {sub z} = 1/2. The equations are converted to a matrix equation with a specially tunedmore » 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.« less

  • We apply Pauli-Villars regularization and discrete light-cone quantization to the nonperturbative solution of (3+1)-dimensional Yukawa theory in a single-fermion truncation. Three heavy scalars, including two with negative norm, are used to regulate the theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of a new, indefinite-metric Lanczos algorithm. Various observables are extracted from the wave functions, including average multiplicities and average momenta of constituents, structure functions, and a form factor slope.

  • ;
    It is proposed that field theories quantized in a curved space-time manifold can be conveniently regularized and renormalized with the aid of Pauli-Villars regulator fields. The method avoids the conceptual difficulties of covariant point-separation approaches, by starting always from a manifestly generally covariant action, and the technical limitations of the dimensional reqularization approach, which requires solution of the theory in arbitrary dimension in order to go beyond a weak-field expansion. An action is constructed which renormalizes the weak-field perturbation theory of a massive scalar field in two space-time dimensions--it is shown that the trace anomaly previously found in dimensional regularizationmore » and some point-separation calculations also arises in perturbation theory when the theory is Pauli-Villars regulated. One then studies a specific solvable two-dimensional model of a massive scalar field in a Robertson-Walker asymptotically flat universe. It is shown that the action previously considered leads, in this model, to a well defined finite expectation value for the stress-energy tensor. The particle production (less than 0 in/vertical bar/theta/sup mu nu/(x,t)/vertical bar/0 in greater than for t ..-->.. + infinity) is computed explicitly. Finally, the validity of weak-field perturbation theory (in the appropriate range of parameters) is checked directly in the solvable model, and the trace anomaly computed in the asymptotic regions t..-->.. +- infinity independently of any weak field approximation. The extension of the model to higher dimensions and the renormalization of interacting (scalar) field theories are briefly discussed.« less

  • We apply Pauli--Villars regularization and discrete light-cone quantization to the nonperturbative solution of a (3+1)-dimensional model field theory. The matrix eigenvalue problem is solved for the lowest-mass state with use of the complex symmetric Lanczos algorithm. This permits the calculation of each Fock-sector wave function, and from these we obtain values for various quantities, such as average multiplicities and average momenta of constituents, structure functions, and a form factor slope.