Although less ubiquitous than the gauge ambiguities present under matter truncation, it should be noted that the truncation of photonic modes also leads to gauge ambiguities that can be resolved in a manner similar to the process discussed in Sect. III B . However, unlike in the case of matter truncation, for mode truncation, the dipole gauge Hamiltonian leads to ambiguities. To see this, recall how Ĥp•A and Ĥd•E can be written in terms of the PZW operator.