The Feynman–Schwinger Representation in QCD

Simonov, Yu. A.; Tjon, J.A.

doi:10.1006/aphy.2002.6282

Cited by 63 publications

(64 citation statements)

References 78 publications

(115 reference statements)

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“…In this paper we will discuss another method, which is based on the path integral formulation of Feynman and Schwinger [1,2]. It was initiated by Simonov and collaborators [3,4,5,6,7,8,9] in their study of quantum chromo-dynamics (QCD).…”

Section: Introductionmentioning

confidence: 99%

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

2005

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In this paper we present a summary of results obtained for scalar field theories using the Feynman-Schwinger (FSR) approach. Specifically, scalar QED and χ 2 φ theories are considered. The motivation behind the applications discussed in this paper is to use the FSR method as a rigorous tool for testing the quality of commonly used approximations in field theory. Exact calculations in a quenched theory are presented for one-, two-, and three-body bound states. Results obtained indicate that some of the commonly used approximations, such as Bethe-Salpeter ladder summation for bound states and the rainbow summation for one body problems, produce significantly different results from those obtained from the FSR approach. We find that more accurate results can be obtained using other, simpler, approximation schemes.

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Section: Introductionmentioning

confidence: 99%

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

2005

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“…One can verify using the Fock-Feynman-Shwinger representation [6] for the Green function expansion (6) that the factorization of the second term in (7) is valid. Terms proportional toW…”

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confidence: 97%

“…come from the first and third terms in (6). The following approximate expression is valid within the accuracy considered,…”

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confidence: 99%

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A short-distance quark-antiquark potential

Бадалян

Kuzmenko

2004

Phys. Atom. Nuclei

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Leading terms of the static quark-antiquark potential in the background perturbation theory are reviewed, including perturbative, nonperturbative and interference ones. The potential is shown to describe lattice data at short quark-antiquark separations with a good accuracy.1. The static quark-antiquark potential was calculated with high accuracy in lattice QCD some years ago [1]. It was shown to be well described by the phenomenological Coulomb+linear Cornell potential at sufficiently large quark-antiquark separations, R > ∼ 0.2 fm. At smaller distances the Cornell potential is not applicable. The region 0.03 fm ≤ R ≤ 0.22 fm was studied in quenched lattice theory in detail [2], and the conclusion was made that the standard perturbative theory expansion in coupling constant does not yield appropriate description of lattice results, at least in one-and two-loop approximations. As is known, next terms of the asymptotic coupling expansion depend on the renormalization scheme, and so the corresponding static potential does. One can argue that the standard perturbative theory fails because this region is close to the unphysical Landau pole of the strong coupling.We consider the static quark-antiquark potential in the background perturbation theory (BPT) [3]. This potential incorporates both the features of the standard perturbative potential at tiny distances, R < ∼ 0.05 fm, and of the Cornell potential at R > ∼ 0.4 fm due to taking nonperturbative background field effects into account. After brief review of leading background potential terms we present our results concerning the behavior of the potential at short distances and its comparison with the lattice [4].2. The gluon field A µ in BPT is divided into the dynamical perturbative part a µ and the background nonperturbative field B µ ,The background field, in which perturbative valence gluons propagate, results in the vacuum condensate creation. The static potential has to be calculated using the vacuum averaged Wilson loop for the quark-antiquark pair. The BPT Wilson loop expansion in the field a µ has the form [3] W (B + a) = W (B) + ∞ n=1

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“…Therefore, it is equally suitable for the perturbative as well as nonperturbative calculations [22]. The nonperturbative calculations within the the worldlines approach could be compared with the results obtained in lattice QCD and other nonperturbative frameworks.…”

Section: Introductionmentioning

confidence: 99%

Soft-gluon resummation in quark-vector boson vertex at high energy

Cherednikov

2005

Eur. Phys. J. A

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Abstract. Resummation of the soft gluon radiative corrections for the quark-vector boson vertex is performed within the path-integral (world-line) approach. The leading order expression for the vacuum averaged Wilson integral for an arbitrary gauge field is found in n-dimensional space-time. The cusp anomalous dimension of the color non-singlet Sudakov form factor of on-mass-shell quark is calculated in an arbitrary covariant gauge in the one-loop order, and the leading double-logarithmic asymptotical behavior is obtained from the corresponding evolution equation.

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The Feynman–Schwinger Representation in QCD

Cited by 63 publications

References 78 publications

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

Nonperturbative dynamics of scalar field theories through the Feynman-Schwinger representation

A short-distance quark-antiquark potential

Soft-gluon resummation in quark-vector boson vertex at high energy

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