This can also be understood as the PZW operator boosting the photonic momentum pc by 2ω c /ℏ μA 0 . The "d • E" Hamiltonian can also be viewed as effectively using the Poincaré gauge, where the vector potential under the Coulomb gauge upon PZW transformation gives the new vector potential A ′ ∥ (r) = -∇ enforces the vector potential to be perpendicular to the r vector everywhere (where the radial component of the vector potential is forced to be zero). The "d • E" Hamiltonian is often referred to as the dipole gauge (where beyond the dipole approximation should be referred to as the multi-polar gauge ) or the lengthgauge due to μ linearly depending on position.