Spectral theory of Pauli-Fierz Hamiltonians I.
Jan Derezinski, Vojkan Jaksic
We study spectral properties of
Pauli-Fierz Hamiltonians which
used to describe
the interaction of a small quantum system with
a bosonic free field.
We give precise estimates on the location and
multiplicity of the singular spectrum of such Hamiltonians.
Applications of these estimates, which will
be discussed elsewhere, concern spectral and
ergodic theory of non-relativistic QED.
has two ingredients: the Feshbach method, which is developed
in an abstract framework, and the Mourre method
applied to the Hamiltonian restricted to the sector orthogonal
to the vacuum.
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This paper has now been published in
J. Funct. Anal. 180 (2001), no. 2, 243--327.