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I was reading the part of QuantumFieldTheory where you check if a particle could exist at x=0 to x=x in space-like plane of a light-cone, therefore if non-zero result, quantum mechanics becomes incompatible with general relativity.But I could not understand the complex integration. The whole problem is below, I had to upload the screenshot, as I do not know how to use this message box to write equations:

enter image description here

I hope I had provided enough information about the question,(by now I've learnt how to use the math_editor :) ) what I'd like to know is, how did the $e^{i|x||p|}$ of the third to the last line has become $e^{-m|x|} \int_{m}^\infty dzz e^{-(z-m)}$ in the last line, and $e^{-it {\sqrt |p|^2 - m^2}}$ of the same, third to the last line, has become $sinh(t{\sqrt z^2 - m^2 })$ in the last line. This is what I meant in my original question, when I said how did the integral developed, especially the parts that mapped on the contour.

appreciated for help and apologised for any mistake both in advance kind regards

I have editted the picture and corrected the typos, there is absolutely no mistake in the question, at least no mistake in my part, as I've copied the page of the book correctly. For those who might own the book; Quantum Field Theory for the gifted amateur by Tom Lancaster and Stephen J. Blundell, page75, equation 8.18 and page 76, eqt. 8.19 with Figure 8.3

Note: If someone can embed the image again, instead of a plain link, I'd appreciate

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closed as unclear what you're asking by Winther, Xander Henderson, Lord Shark the Unknown, Taroccoesbrocco, user99914 Jul 29 '18 at 8:42

Please clarify your specific problem or add additional details to highlight exactly what you need. As it's currently written, it’s hard to tell exactly what you're asking. See the How to Ask page for help clarifying this question. If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ Please see math.meta.stackexchange.com/questions/5020/… $\endgroup$ – 高田航 Jul 27 '18 at 18:24
  • $\begingroup$ Thank you, but for now,I'm going to wait until someone tells me(if what i did is against the forum rules) to write it specifically with the text editor, as I've already provided a readable version of the question(as an image) and its killing me to write it once more.I'm going to try my chance $\endgroup$ – bergdi Jul 27 '18 at 18:37
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    $\begingroup$ MathJax is easier to read than your image. $\endgroup$ – mvw Jul 27 '18 at 19:02
  • $\begingroup$ There is no conversion of complex variables to polar coordinates. Have you ever used Jacobians? $\endgroup$ – Andrei Jul 27 '18 at 20:57
  • $\begingroup$ I don't understand the substitution from the third to last to second to last line. It's not $p=\pm iz$. There are a lot of typos and perhaps outright errors, too, so overall, I'm skeptical of this work. $\endgroup$ – zahbaz Jul 29 '18 at 2:24