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We consider a Pauli-Fierz Hamiltonian for a particle coupled to a photonfield. We discuss the effects of the increase of the binding energy andenhanced binding through coupling to a photon field, and prove that botheffects are the results of the existence of the ground state of the self-energyoperator with total momentum $P = 0$.Comment: 14 pages, Latex. Final version, accepted for publication in J. Math.  Phy

The increase of binding energy and enhanced binding in nonrelativistic QED