Why does the Schwinger parameter correspond to proper length?

[Dilatino]

I have just learned from nice article

http://motls.blogspot.com/2013/12/edward-witten-what-every-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 don't see this, so can somebody give a derivation/further explanation?

 

[Spinnor]

Using Wolfram Alpha,

http://www.wolframalpha.com/input/?i=integral+from+0+to+infinity+of+(+exp[-at])dt

input,

integral from 0 to infinity of ( exp[-at])dt

output,

1/a

 

[fzero]

There's a nice clear presentation of the argument given in the 1951 Schwinger paper at http://www.thetangentbundle.net/wiki/Quantum_field_theory/Schwinger_proper_time_formalism. Post back if that doesn't help.