Observable effects and parametrized scaling limits of a model in nonrelativistic quantum electrodynamics.

Scaling limits of the Hamiltonian H of a system of N charged particles coupled to a quantized radiation field are considered. Ultraviolet cutoffs, ...[sub 1],…,...[sub N], are imposed on the radiation field and the Coulomb gauge is taken. It is the so-called Pauli-Fierz model in nonrelativistic quantum electrodynamics. We mainly consider two cases: (i) all the ultraviolet cutoffs are identical, ...[sub 1] = … = ...[sub N], (ii) supports of ultraviolet cutoffs have no intersection, supp ...[sub i]∩supp...=Ø, i &ne j. The Hamiltonian acts on L²(R[sup dN])⊗F, where F is a symmetric Fock space, and has the form H=H[sub e1]⊗1 + B + 1 ⊗ H[sub quad]. Here H[sub el] denotes a particle Hamiltonian, H[sub quad] a quadratic field operator, and B an interaction term. The scaling is introduced as H(κ)=H[sub el]⊗1+ κ[sup l]B+κ²1⊗H[sub quad], where κ is a scaling parameter and l ≤ 2 a parameter of the scaling. Performing a mass renormalization we consider the scaling limit of H(κ) as κ→∞ in the strong resolvent sense. Then effective Hamiltonians H[sub eff] in L²(R[sup dN]) infected with reaction of effect of the radiation field is derived. In particular (1) effective Hamiltonians with an effective potential for l = 2, and (2) effective Hamiltonians with an observed mass for l= 1, are obtained. [ABSTRACT FROM AUTHOR]