Imaginary Time and Path Integrals?

LarryS
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Steven Hawking writes in A Brief History of Time that time itself must sometimes have an imaginary component in order for Feynman's Sum-Over-Histories approach to work. Why, in a nutshell, is this so? Thanks in advance.
 
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Convergence of the integral.
 
It is wick rotation, please google "wick rotation",
you also can find wick rotation in Wiki
 

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