Truncation of Schwinger-Dyson equations and the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mfrac><mrow><mn>1</mn></mrow><mrow><mi>N</mi></mrow></mfrac></math></span> expansion in the <span class="aps-inline-formula"><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi mathvariant="normal">O</mi><mn></mn><mo>(</mo><mi>N</mi><mo>)</mo><mn></mn></math></span> model

C. L. Korpa; Jitendra C. Parikh; Philip J. Siemens

doi:10.1103/PhysRevD.41.1276

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Truncation of Schwinger-Dyson equations and the $\frac{1}{N}$ expansion in the $O (N)$ model

C. L. Korpa, Jitendra C. Parikh^*, and Philip J. Siemens

Department of Physics, Oregon State University, Corvallis, Oregon 97331

^*On leave from Physical Research Laboratory, Navrangpura, Ahmedabad, 380009, India.

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Phys. Rev. D 41, 1276 – Published 15 February, 1990

DOI: https://doi.org/10.1103/PhysRevD.41.1276

Abstract

We use the $O (N)$ model as a nonperturbative example to study the effect of truncating the Schwinger-Dyson sequence of equations. We show that truncation of this hierarchy leads in the $O (N)$ model to solutions for the propagators and vertex functions correct to a definite power of $\frac{1}{N}$ . The procedure can be used to generate a systematic expansion in $\frac{1}{N}$ for an arbitrary Green's function of the model.

References (12)

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D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974)
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R. G. Root, Phys. Rev. D 11, 831 (1975)

[c1] F. J. Dyson, Phys. Rev. 75, 1736 (1949) J. Schwinger, Proc. Natl. Acad. Sci. USA 37, 452 (1951) ibid.37, 455 (1951)

[c2] S. Mandelstam, Phys. Rev. D 20, 3223 (1979)

[c3] E. Bagan and M. R. Pennington, Phys. Lett. B 220, 453 (1989)

[c4] K.-I. Kondo, Y. Kikukawa, and H. Mino, Phys. Lett. B 220, 270 (1989)

[c5] P. J. Siemens, M. Soyeur, G. D. White, L. J. Lantto, and K. T. R. Davies, Phys. Rev. C 40, 2641 (1989)

[c6] R. Jackiw, Phys. Rev. D 9, 1686 (1974)

[c7] S. Coleman. R. Jackiw, and H. D. Politzer, Phys. Rev. D 10, 2491 (1974)

[c8] R. G. Root, Phys. Rev. D 10, 3322 (1974)

[c9] L. F. Abbott, J. S. Kang, and H. J. Schnitzer, Phys. Rev. D 13, 2212 (1976)

[c10] D. J. Gross and A. Neveu, Phys. Rev. D 10, 3235 (1974)

[c11] B. Rosenstein and B. J. Warr, Phys. Lett. B 218, 465 (1989) B. Rosenstein, B. J. Warr, and S. H. Park, Phys. Rev. Lett. 62, 1433 (1989) Phys. Lett. B 219, 469 (1989)

[c12] R. G. Root, Phys. Rev. D 11, 831 (1975)

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Truncation of Schwinger-Dyson equations and the $\frac{1}{N}$ expansion in the $O (N)$ model

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Truncation of Schwinger-Dyson equations and the 1N expansion in the O(N) model

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References (12)

Truncation of Schwinger-Dyson equations and the $\frac{1}{N}$ expansion in the $O (N)$ model