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

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

1995-06-28

arxiv.org/abs/hep-th/9506188v1

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, includes 4-uuencoded figures, uses revtex one minor corection in the tex source to include properly fig

Scientific paper

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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