+ \frac{{\bf k} \times {\bf \hat S}}{k^2 } = i\partial _{\bf k}  + \frac{{\bf k} \times {\bf \hat S}}{k^2 }~.$$ The modified position operator (\[eqn:3\]) has been considered in the context of photon localization and Berry phase [@Pryce; @Photon; @Hawton]. It describes the observable center of gravity of the field and brings about the space non-commutativity with the monopole term in ${\bf k}$-space: $$\label{eqn:4}
\left[ {\hat r'_i ,\hat r'_j } \right] =  - i\epsilon _{ijl} \hat \sigma \frac{k_l }{k^3 }~.$$ The operators ${\bf \hat L'}$ and ${\bf \hat S'}$ do not satisfy the $so(3)$ AM algebra and have unusual commutation relations: $$\label{eqn:5}
\left[ {\hat S'_i ,\hat S'_j } \right] = 0,~\left[ {\hat L'_i ,\hat L'_j } \right] = i\epsilon _{ijl} (\hat L'_l -\hat S'_l),~
\left[ {\hat L'_i ,\hat S'_j } \right] = i\epsilon _{ijl} \hat S'_l.$$ At the same time, the modified operators transform as vectors under rotations: $\left[ {\hat J_i ,\hat O'_j } \right] = i\epsilon _{ijl} \hat O'_l$, ${\bf \hat O'} = {\bf \hat L'}$, ${\bf \hat S'}$, and ${\bf \hat r'}$. The commutation relations (\[eqn:5\]) unveil the similarity of operators ${\bf \hat L'}$ and ${\bf \hat S'}$ to those obtained for the second-quantized fields in [@EN]. Although 