Pion-Nucleon Scattering in Kadyshevsky Formalism: I Meson Exchange Sector

In a series of two papers we present the theoretical results of πN/meson-baryon scattering in the Kadyshevsky formalism. In this paper the results are given for meson exchange diagrams. On the formal side we show, by means of an example, how general couplings, i.e. couplings containing multiple derivatives and/or higher spin fields, should be treated. We do this by introducing and applying the Takahashi-Umezawa and the Gross-Jackiw method. For practical purposes we introduce the P̄ method. We also show how the Takashashi-Umezawa method can be derived using the theory of Bogoliubov and collaborators and the Gross-Jackiw method is also used to study the n-dependence of the Kadyshevsky integral equation. Last but not least we present the second quantization procedure of the quasi particle in Kadyshevsky formalism.