A non-perturbative method of calculation of Green functions
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 φ4d-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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