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Variational Solution of the Gross-Neveu model I. the Large-$N$ Limit

C. Arvanitis·F. Geniet·A. Neveu
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Abstract

In this first paper we begin the application of variational methods to renormalisable asymptotically free field theories, using the Gross-Neveu model as a laboratory. This variational method has been shown to lead to a numerically convergent sequence of approximations for the anharmonic oscillator. Here we perform a sample calculation in lowest orders, which shows the superficially disastrous situation of variational calculations in quantum field theory, and how in the large-$N$ limit all difficulties go away, as a warm up exercise for the finite-$N$ case and for QCD.

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C. Arvanitis, F. Geniet, A. Neveu. 1995-06-28. Variational Solution of the Gross-Neveu model I. the Large-$N$ Limit. https://arxiv.org/abs/hep-th/9506188

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