On the Smooth Feshbach-Schur Map

TL;DR

This paper analyzes and generalizes the smooth Feshbach map, a tool used in quantum electrodynamics, clarifying its mathematical properties and extending its applicability to non-selfadjoint operators.

Contribution

It provides a detailed analysis and generalization of the smooth Feshbach map, enhancing its algebraic and analytic understanding and broadening its scope.

Findings

Clarified algebraic and analytic properties of the smooth Feshbach map.

Generalized the map to non-selfadjoint partition operators.

Enhanced the mathematical framework for applications in quantum electrodynamics.

Abstract

A new variant of the Feshbach map, called smooth Feshbach map, has been introduced recently by Bach et al., in connection with the renormalization analysis of non-relativistic quantum electrodynamics. We analyze and clarify its algebraic and analytic properties, and we generalize it to non-selfadjoint partition operators $\chi$ and $\chib$.