Abstract
The use of variational method in functional integral approach is discussed for fermion and boson systems with Coulomb interaction. The formal general expression of thermodynamic potential is obtained by Feynman path integral technique and representation of Coulomb interaction with functional integrals. Introduced additional complex field show to transform the problem to calculation of functional integrals containing third order vertices. The thermodynamic potential can be found from variational principle with respect to field cumulants. The calculation of the equation of state and critical properties is demonstrated for symmetrical plasma by variation of finite number of parameters in the propagator.
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