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 ${\varphi }_d^4$-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.

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

References in corpus (1)

• Connected Green function approach to ground state symmetry breaking in ${\Phi }_{1+1}^4$-theory

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• Dynamical Symmetry Breaking and Negative Cosmological Constant
• On solving Schwinger-Dyson equations for non-Abelian gauge theory