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:
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