- 97-268 Bach, V., Frohlick, J., Sigal, I.M., Soffer, A.
- Positive Commutators and Spectrum of Nonrelativistic QED
May 14, 97
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Abstract. In this paper we consider the Hamiltonian of the standard
model of non-relativistic QED. In this model non-relativistic
quantum particles interact with
quantized electro-magnetic field and their interaction
is subjected to an ultra-violet cut-off.
We prove absence of excited states and absolute continuity
of the spectrum for sufficiently small charges under conditions
on the coupling functions which milder than those of
We use the method of positive commutators with
the ``conjugate'' operator deformed appropriately
in order to accomodate the interaction term.