Ground States for Infrared Renormalized Translation-Invariant Non-Relativistic QED

We consider a translation-invariant Pauli–Fierz model describing a non-relativistic charged quantum mechanical particle interacting with the quantized electromagnetic field. The charged particle may be spinless or have spin one half. We decompose the Hamiltonian with respect to the total momentum into a direct integral of so-called fiber Hamiltonians. We perform an infrared renormalization, in the sense of norm resolvent convergence, for each fiber Hamiltonian, which has the physical interpretation of removing an infinite photon cloud. We show that the renormalized fiber Hamiltonians have a ground state for almost all values for the total momentum with modulus less than one.