arXiv subjects

V. E. Rochev

Publications and source records attributed to V. E. Rochev.

21 records · Page 2Linked to original sources

arXiv1997

A non-perturbative method of calculation of Green functions

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 $ϕ^4_d$-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.

hep-th↗

arXiv1995

Singular Perturbations in Quantum Field Theory

In this talk we discuss a new approximation scheme for non-perturbative calculations in a quantum field theory which is based on the fact that the Schwinger equation of a quantum field model belongs to the class of singularly perturbed equations. The self-interacting scalar field and the Gross-Neveu model are taken as the examples and some non-perturbative solutions of an equation for the propagator are found for these models. The application to QCD is also discussed.

hep-th↗

arXiv1995

Schwinger Equation as Singularly Perturbed Equation

A new approximation scheme for non-perturbative calculations in a quantum field theory is proposed. The scheme is based on investigation of solutions of the Schwinger equation with its singular character taken into account. As a necessary supplementary boundary condition the Green functions' connected structures correspondence principle is used. Besides the usual perturbation theory expansion which is always available as a particular solution of our scheme some non-perturbative solutions of an equation for the propagator are found in the model of a self-interacting scalar field.

hep-th↗