Unruh Effect (1+1)D: Understanding Equation 5.68

[thatboi]

Hi all,
I am trying to work through the Unruh Effect for the (1+1)-dimensional massive scalar field case and came across the paper I attached. However, I am trying to derive equation 5.68, but am greatly struggling with the prefactor on the left hand side. When comparing the left hand side to (5.64), it is clear that there is an extra factor of \frac{1}{\sqrt{2\pi}} that seems to appear out of nowhere. Can someone provide assistance? Thank you.

 

[PeterDonis]

came across the paper I attached.

Can you give a link to where you obtained it?

 

[Demystifier]

Perhaps (5.42) could be the key.