# Why does the Schwinger parameter correspond to proper length?

by Dilatino
Tags: correspond, length, parameter, propagaor, proper, quantum field theory, schwinger
 P: 5 I have just learned from nice article http://motls.blogspot.com/2013/12/ed...y-quantum.html that the propagator of a massive particle can be rewritten as an integral over the so-called Schwinger parameter t as $$\frac{1}{p^2 + m^2} = \int\limits_0^\infty dt \exp(-t(p^2 + m^2))$$ In addition, in the blog article it is said that this Schwinger parameter p can be interpreted as the proper length of the propagator. I dont see this, so can somebody give a derivation/further explanation?
 P: 1,362 Using Wolfram Alpha, http://www.wolframalpha.com/input/?i...%5B-at%5D%29dt input, integral from 0 to infinity of ( exp[-at])dt output, 1/a
 Sci Advisor HW Helper PF Gold P: 2,606 There's a nice clear presentation of the argument given in the 1951 Schwinger paper at http://www.thetangentbundle.net/wiki...time_formalism. Post back if that doesn't help.

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