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cello
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In Schwinger's classic http://dx.doi.org/10.1103/PhysRev.82.664" on pair production, he inserted an infinitesimal to get the desired pair production rate. (On page 13, he said: "We shall now simply remark that, to extend our results to pair-production fields, it is merely necessary to add an infinitesimal negative imaginary constant to the denominator of Eq. (6.30) ")
Also I found a pedagogical http://dx.doi.org/10.1119/1.19313" in which the author said "Defining the integration contour by infinitesimal semicircular deviations into the upper half plane from the straight line path (in order to guarantee exponential decay)." It seems that this is a choice made by hand.
Can anyone explain in detail the justification for this epsilon? I'm aware of the epsilon we added to the time (or the mass) when doing path integral, but I can't see if the epsilon in Schwinger's paper is of the same nature.
You can download the two papers I mentioned http://ifile.it/u9smtwa", if you don't have the access.
Also I found a pedagogical http://dx.doi.org/10.1119/1.19313" in which the author said "Defining the integration contour by infinitesimal semicircular deviations into the upper half plane from the straight line path (in order to guarantee exponential decay)." It seems that this is a choice made by hand.
Can anyone explain in detail the justification for this epsilon? I'm aware of the epsilon we added to the time (or the mass) when doing path integral, but I can't see if the epsilon in Schwinger's paper is of the same nature.
You can download the two papers I mentioned http://ifile.it/u9smtwa", if you don't have the access.
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