Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1996-06-25
J.Phys.A30:3671-3680,1997
Physics
High Energy Physics
High Energy Physics - Theory
13 pages, Plain LaTex, no figures, some discussion of results for anharmonic oscillator and a number of references are added,
Scientific paper
10.1088/0305-4470/30/10/037
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.
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