# How does the Wilson Line change under time reversal?

1. Jan 22, 2015

### Chenkb

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??
$-ig\int_{-\vec a_\perp}^{-\vec b_\perp} dx_\perp \cdot [-A_\perp(x_\perp)]$

Last edited: Jan 22, 2015
2. Jan 27, 2015