Kallen-Lehmann representation for Spinor-Scalar Loops in de Sitter Space-time. Spectral equations

Abstract: Compact formulas (1), (28) presented in this paper permit to formulate the Kallen-Lehmann harmonic decompositions of the products of two spinor and of spinor and scalar harmonic functions in AdS and Wightman functions in dS spaces; the correct flat space limit of the corresponding Kallen-Lehmann densities is demonstrated. Also in Sec. 4 the relatively simple, suitable for calculations Kallen-Lehmann representations of the real parts of spinor and scalar one-loop self-energies in Yukawa model in dS space-time are proposed, and corresponding spectral equations in the chain approximation are written down.