We address the problem of finding a product picture for QED — i.e. a reformulation in which (formally) it has a total Hamiltonian arising as a sum of a free electromagnetic Hamiltonian, a free Dirac Hamiltonian and an interaction term, acting on a Hilbert space which is a subspace (the physical subspace) of the full tensor product of an electron/positron Hilbert space and an electromagnetic-field Hilbert space. The traditional Coulomb gauge formulation of QED isn’t a product picture in this sense because in it, the longitudinal part of the electric field is a function of the Dirac field. We exhibit a product picture and prove (at a formal level) its equivalence with Coulomb gauge QED. We also point out a number of its features.

Reference: arXiv:2204.01177, and for more details, Sections 4 and 5 of arXiv:2003.07473