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Rigorous construction of planar diagram field theories in four dimensional Euclidean space

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Abstract

Asymptotically free quantum field theories with planar Feynman diagrams [such as SU(∞) gauge theory] are considered in 4 dimensional Euclidean space. It is shown that if all particles involved have non-vanishing masses and if the coupling constant(s) γ (org 2) are small enough (λ≦λcrit), then an absolutely convergent procedure exists to obtain Green functions that uniquely solve the Dyson-Schwinger equations.

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Authors and Affiliations

  1. Institute for Theoretical Physics, Princetonplein 5, P.O. Box 80.006, NL-3508 TA, Utrecht, The Netherlands

    Gerard 't Hooft

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  1. Gerard 't Hooft
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Communicated by A. Jaffe

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't Hooft, G. Rigorous construction of planar diagram field theories in four dimensional Euclidean space. Commun.Math. Phys. 88, 1–25 (1983). https://doi.org/10.1007/BF01206876

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  • DOI: https://doi.org/10.1007/BF01206876

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