Theory of direct four-fermion interaction

A solution is obtained of the ''parquet'' equations for the vertex GITA (p1, p2, p3, p4) of direct four-fermion interaction in space of d=2+epsilon dimensions. A requirement for the existence of the solution is symmetry of the type of SU(2) invariance of interaction and positiveness of the coupling constant G. The solution is scale-invariant for high energies such as Gp2 >>1 and corresponds to a stable fixed point of the Gell-Mann-Low equations. It is shown that a similar solution satisfies approximately a set of equations in real four-dimensional d=4 space and all integrals in the equations are found to be convergent. The so-called ''nonparquet'' terms, which are not taken into account in the equations, are estimated by means of the solution obtained. It is shown that they are numerically small. The solution may be employed as a zero approximation of the interaction method for a set of exact equations