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

TL;DR

This paper develops spectral formulas for spinor-scalar loops in de Sitter space, connecting harmonic decompositions with physical divergences and providing calculable representations for self-energies.

Contribution

It introduces compact Kallen-Lehmann formulas for harmonic decompositions on AdS and dS spaces, linking pole structures to divergences and proposing spectral equations for self-energies.

Findings

Correct flat space limits of Kallen-Lehmann densities demonstrated

Connection between poles and late-time divergences established

Spectral equations for conformal dimensions derived

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 on AdS and Wightman functions on dS spaces; the correct flat space limits of the corresponding Kallen-Lehmann densities is demonstrated, the connection between poles of the Kallen-Lehmann density and the late-time divergence of the spinor-scalar loop is traced in the Yukawa model with light scalar field. 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 on dS space-time are proposed, and corresponding spectral equations for conformal dimensions in the chain approximation are written down.