Time-ordered exponential on the complex plane and Gell-Mann -- Low   formula as a mathematical theorem
  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. 
Shinichiro Futakuchi and Kouta Usui
math.FA hep-th math-ph math.MP