The role of interaction vertices in bound state calculations

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In recent studies of the one and two-body problem for scalar interactions it was shown that crossed ladder and ''crossed rainbow'' (for the one-body case) exchanges play a crucial role in nonperturbative dynamics. In this letter we use exact analytical and numerical results to show that the contribution of vertex dressings to the two-body bound state mass for scalar QED are canceled by the wavefunction normalization. This proves, for the first time, that the mass of a two-body bound state given by the full theory can be obtained by summing only ladder and crossed ladder diagrams using a bare vertex ... continued below

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Savkli, Cetin; Gross, Franz & Tjon, John February 1, 2001.

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In recent studies of the one and two-body problem for scalar interactions it was shown that crossed ladder and ''crossed rainbow'' (for the one-body case) exchanges play a crucial role in nonperturbative dynamics. In this letter we use exact analytical and numerical results to show that the contribution of vertex dressings to the two-body bound state mass for scalar QED are canceled by the wavefunction normalization. This proves, for the first time, that the mass of a two-body bound state given by the full theory can be obtained by summing only ladder and crossed ladder diagrams using a bare vertex and a constant dressed mass. We also discuss the implications of the remarkable cancellation between rainbow and crossed rainbow diagrams that is a feature of one-body calculations.

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297 Kilobytes pages

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  • Report No.: JLAB-THY-02-08
  • Report No.: DOE/ER/40150-1989
  • Report No.: WM-02-02
  • Grant Number: FG02-97ER41032
  • Grant Number: AC05-84ER40150
  • Office of Scientific & Technical Information Report Number: 791342
  • Archival Resource Key: ark:/67531/metadc734184

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  • February 1, 2001

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  • Oct. 19, 2015, 7:39 p.m.

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  • Feb. 5, 2016, 9:50 p.m.

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Savkli, Cetin; Gross, Franz & Tjon, John. The role of interaction vertices in bound state calculations, article, February 1, 2001; Newport News, Virginia. (digital.library.unt.edu/ark:/67531/metadc734184/: accessed October 21, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.