How does the Wilson Line change under time reversal?

  • Thread starter Chenkb
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  • #1
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Textbooks tell us that a four vector under time reversal changes as ##x^\mu \to \tilde x^\mu = x_\mu##, and ##i \to -i##. The gluon field changes as ##A^\mu(x) \to A_\mu(-\tilde x)##.
My question is how does the following integral (the wilson line in the perpendicular direction) change unter time reversal?
##\mathcal{P} \exp\{ig\int_{\vec a_\perp}^{\vec b_\perp} dx_\perp \cdot A_\perp(x_\perp)\}##
Can it be the following way??
##-ig\int_{-\vec a_\perp}^{-\vec b_\perp} dx_\perp \cdot [-A_\perp(x_\perp)]##
 
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Answers and Replies

  • #2
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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

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