# Question on the Gell-Mann Low equation

Question on the Gell-Mann Low Equation.

In this paper, http://arxiv.org/abs/1205.3365, page 21, the author argues that if:

t →∞(1-iϵ), all the terms in equation (193) goes to zero, except the first term.

Can anyone explain this to me?

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If you substitute $t\rightarrow \tau (1-i\epsilon)$ in your eq. (193), then the exponent is no longer a pure phase (i.e. complex number wuth modulus =1). All the terms receive a factor of type $e^{-\tau E_n}$. All these terms go to zero, as $\tau \rightarrow \infty$, but since author says $E_n > E_0$ for all $n>0$, then the first term goes to zero slower than all other terms. Thus we keep only this first term. If you understand now, then you can make it your own answer, it is ok to answer your questions. –  au700 Nov 29 '12 at 14:17