New form of kernel in equation for Nakanishi function

The Bethe-Salpeter amplitude $\mathrm{\ensuremath{\Phi}}(k,p)$ is expressed, by means of the Nakanishi integral representation, via a smooth function $g(\ensuremath{\gamma},z)$. This satisfies canonical equation $g=Ng$. However, calculations kernel $N$ in this equation, presented previously, were restricted to one-boson exchange and, depending on method, dealt with complex multivalued functions. Although these difficulties are surmountable, practice, they complicate finding unambiguous result. In present work, an expression for terms real functions derived. For scalar exchange, explicit formula found. With and kernel, binding energies, calculated reproduced. Their finding, as well calculation Minkowski space, become no more difficult than Euclidean one. method can be generalized any given irreducible Feynman graph. generalization illustrated example cross-ladder kernel.