Time-ordered exponential on the complex plane and Gell-Mann -- Low formula as a mathematical theorem

TL;DR

This paper rigorously proves the Gell-Mann--Low formula using complex time evolution operators, with applications to quantum electrodynamics, providing a solid mathematical foundation for these quantum field theory concepts.

Contribution

It offers a rigorous mathematical proof of the Gell-Mann--Low formula via complex time-ordered exponentials, extending its validity to quantum electrodynamics with cutoffs.

Findings

Rigorous proof of Gell-Mann--Low formula using complex time evolution

Application of abstract results to quantum electrodynamics with cutoffs

Mathematically solid foundation for complex time-ordered exponentials in quantum theory

Abstract

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann -- Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs.