[![enter image description here][1]][1]

I found this in the book Geometric Phase in Quantum Systems by A. Bohm et al.

Where the position space representation of the momentum operator carries a (Where exactly my doubt is) coefficient of 1-form with the condition 

$$\partial_i w_j - \partial_j w_i =0 \implies dw=0$$

The author(s) argued about $poincare \ lemma$ and how, for $R^m$ configuration space the term can be $gauged \ away$

I understand usual momentum operator representation without this 1-form, and this is very non-trivial for me. 

Can someone please explain me how this comes and what it means in details?

  [1]: https://i.sstatic.net/L2jaq.png