Topics in Kadyshevsky Field Theory

Abstract: In these notes we deal with several field theoretical topics in the framework of the Quantum Field Theory as developed by Kadyshevsky. The main motivation for studying the Kadyshevsky formalism is that in the kadyshevsky graphs, in contrast with the Feynman graphs, the particles remain on the mass shell. This facilitates the use of phenomenological form factors, {\it e.g.} Gaussian ones. In the first part we construct the second quantised quasi-particle formalism, which is employed to develop the functional integral formalism. In the latter we develop the path-integral, the Schwinger-Symanzik equations, generalised Wightman functions, and the Kadyshevsky reduction formulas. In the second part we cover the topics: (i) the relation between the Feynman and Kadyshevsky perturbation theory, and (ii) the Gross-Jackiw method in the Kadyshevsky formalism. The latter method is applied to the kadyshevsky formalism for interaction Lagrangians with derivatives, in particular for pion-nucleon interactions: (i) pseudo-vector $NNπ$-, (ii) vector $NNρ$-, and (iii) gauge-invariant $Δ_{33}Nπ$ coupling.