Summary: We propose a new method to derive certain higher order estimates in quantum electrodynamics. Our method is particularly convenient in the application to the non-local semi-relativistic models of quantum electrodynamics as it avoids the use of iterated commutator expansions. We re-derive higher order estimates obtained earlier by Fröhlich, Griesemer, and Schlein and prove new estimates for a non-local molecular no-pair operator.

81Q10, 81V10

(Semi-relativistic) Pauli-Fierz operator, no-pair Hamiltonian, higher order estimates, quantum electrodynamics