# Comparator operator in QFT

In Peskin and Shroeder, for a local $$U(1)$$ transformation, the comparator operator is expanded as: $$$$U(x+\epsilon n, x) = 1 -ie\epsilon n^{\mu}A_{\mu} + \mathcal{O}(\epsilon^2) \tag{15.5}$$$$ for $$\epsilon\rightarrow0$$. I am not sure how one arrives at this expression, apart from "feeling" that it should depend on the distance $$\epsilon n^{\mu}$$, thus needing some other vector quantity.

Later, when talking about $$SU(2)$$, they expand $$U$$ as: $$$$U(x+\epsilon n,x) = 1 + ig\epsilon n^{\mu}A^i_{\mu}\frac{\sigma^i}{2}+\mathcal{O}(\epsilon^2). \tag{15.23}$$$$ Where did this sign change come from? The authors also say that $$U$$ can be consistently restricted to be a unitary matrix and because of that, can be expanded as above. How do we know it is possible? This question was already asked here, but the only answer is cyclical.