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

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The discussion focuses on deriving equation 5.68 of the Unruh Effect for a (1+1)-dimensional massive scalar field. The user is struggling with an unexpected prefactor of \frac{1}{\sqrt{2\pi}} on the left side of the equation. They seek clarification on its origin, particularly in relation to equation 5.64. Another participant suggests that equation 5.42 might hold the key to understanding this discrepancy. The conversation emphasizes the need for collaborative problem-solving in theoretical physics.
thatboi
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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.
 

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thatboi said:
came across the paper I attached.
Can you give a link to where you obtained it?
 
Perhaps (5.42) could be the key.
 

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