A non-perturbative method of calculation of Green functions

V. E. Rochev

doi:10.1088/0305-4470/30/10/037

A non-perturbative method of calculation of Green functions

High Energy Physics - Theory 2008-11-26 v2

Authors: V. E. Rochev

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Abstract

A new method for non-perturbative calculation of Green functions in quantum mechanics and quantum field theory is proposed. The method is based on an approximation of Schwinger-Dyson equation for the generating functional by exactly soluble equation in functional derivatives. Equations of the leading approximation and the first step are solved for $\phi^4_d$ -model. At $d=1$ (anharmonic oscillator) the ground state energy is calculated. The renormalization program is performed for the field theory at $d=2,3$ . At $d=4$ the renormalization of the coupling involves a trivialization of the theory.

Keywords

non-perturbative method green functions schwinger-dyson equation quantum field theory renormalization phi^4 model

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@article{arxiv.hep-th/9606155,
  title  = {A non-perturbative method of calculation of Green functions},
  author = {V. E. Rochev},
  journal= {arXiv preprint arXiv:hep-th/9606155},
  year   = {2008}
}

Comments

13 pages, Plain LaTex, no figures, some discussion of results for anharmonic oscillator and a number of references are added, final version published in Journal of Physics A

A non-perturbative method of calculation of Green functions

Abstract

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