It seems to me that the whole fuss about switching to euclidean time to(adsbygoogle = window.adsbygoogle || []).push({});

remove wildly oscillatory behaviour in many integrals found in QFT to be

unnecessary. For instance if we calculate <0|0>j the result is a path

integral / <0|0>[j=0]. However we cheat in our mathematics by demanding that

<0|0>[j=0] is equal to 1. Mathematically <0|0>j=0 is actually some integral

with wildly oscilatory behaviour because we choose to take |0> at t'=+inf

and <0| at t=-inf. It is entirely reasonable to declare the amplitude to be

1 but there is no reason to say that the phase is zero. We could have simply

recognized the phase to be a meaningless quantity undetectable to

experiment. Now going back to <0|0>[j=0], we foolishly choose to integrate

to infinity when in fact all the action happens between t1 and t2, when

j~=0. Therefore, let us simply take the beginning time and the end time to

be large (again quite foolish) but restricted to the condition E0*(t' - t) =

2*pi*N, for some large N. Now all our integrals

end up with no phase contribution due to time evolution outside of [t1,t2].

If we did not artificially contrive t' and t as above, we end up with some

meaningless phase, so be it. Sure its not elegant but its saves a few pages

in your QFT textbook. Am i missing something?

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# Wick rotation

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