  In the standard mean-field treatment of superconductors, the
electron-electron interactions are assumed to be written in terms of local
density operators. However, more general interactions, such as pair-hopping
interactions, may exist or may be generated in a low-energy effective
Hamiltonian. In this work, we study the effect of correlated hopping
interactions toward the electromagnetic response of superconductors. When only
the Hamiltonian after the mean-field approximation is provided, one cannot
unambiguously determine its electromagnetic response whenever such interactions
are allowed. This work demonstrates that such interactions induce additional
terms in the current operator, leading to modifications in the Meissner weight
and optical conductivities that deviate from conventional expectations. These
results underscore the need for caution when incorporating gauge fields into
the BdG Hamiltonian.
