Extracted from(adsbygoogle = window.adsbygoogle || []).push({}); 'At the frontiers of Physics, a handbook of QCD, volume 2',

'...in the physical Bjorken ##x##-space formulation, an equivalent definition of PDFs can be given in terms of matrix elements of bi-local operators on the lightcone. The distribution of quark 'a' in a parent 'X' (either hadron or another parton) is defined as$$f^a_A (\zeta, \mu) = \frac{1}{2} \int \frac{\text{d}y^-}{2\pi} e^{-i \zeta p^+ y^-} \langle A | \bar \psi_a(0, y^-, \mathbf 0) \gamma^+ U \psi_a(0) | A \rangle ,'$$ where $$U = \mathcal P \exp \left( -ig \int_0^{y^-} \text{d}z^- A_a^+(0,z^-, \mathbf 0) t_a \right)$$ is the Wilson line.

My questions are:

1) Where does this definition come from? I'd like to particularly understand in detail the content of the rhs (i.e the arguments of the spinors, why an integral over ##y^-## etc)

2) The review also mentions that in the physical gauge ##A^+=0, U## becomes the identity operator in which case ##f^a_A## is manifestly the matrix element of the number operator for finding quark 'a' in A with plus momentum fraction ##p_a^+ = \zeta p_A^+, p_a^T=0##. Why is ##A^+=0## the physical gauge?

Thanks for any help!

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# A PDFs expressed as matrix elements of bi-local operators

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