Fumio Hiroshima
Observable effects and parametrized 
scaling limits of a model in nonrelativistic quantum electrodynamics
(84K, Latex)

ABSTRACT.  Scaling limits of the Hamiltonian $H$ of a system of $N$ charged particles 
coupled to a quantized radiation field 
are considered. 
Ultraviolet cutoffs, $\la_1,....,\la_N$, are 
imposed on the radiation field and the Coulomb gauge is taken. 
It is so called the Pauli-Fierz model in nonrelativistic quantum electrodynamics. 
We mainly consider two cases: 
(i) all the ultraviolet cutoffs are identical, $\la_1=\cdots=\la_N$, 
(ii) supports of ultraviolet cutoffs have no intersection, 
${\rm supp}\la_i\cap{\rm supp}\laj=\emptyset$, $i\not= j$. 
The Hamiltonian acts on $\LR\otimes\fff$, where $\fff$ is a symmetric Fock space and 
has the form 
$H=\ele\otimes\I+B+\I\otimes\fq$. 
Here $\ele$ denotes a particle Hamiltonian, 
$\fq$ a quadratic field operator, 
and $B$ an interaction term. 
The scaling is introduced as 
$H(\k)=\ele\otimes\I+\k^l B+\k^2\I\otimes\fq$, where $\k$ is a scaling parameter 
and 
$l\leq 2$ a parameter of the scaling. 
Performing a mass renormalization we consider 
the scaling limit of $H(\k)$ as $\k\rightarrow \infty$ 
in the strong resolvent sense. 
Then effective Hamiltonians $\eff$ in $\LR$ 
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.