Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continuity properties of the semi-group and its integral kernel in
  non-relativistic QED   Employing recent results on stochastic differential equations associated with
the standard model of non-relativistic quantum electrodynamics by B. G\"uneysu,
J.S. M{\o}ller, and the present author, we study the continuity of the
corresponding semi-group between weighted vector-valued L^p-spaces, continuity
properties of elements in the range of the semi-group, and the pointwise
continuity of an operator-valued semi-group kernel. We further discuss the
continuous dependence of the semi-group and its integral kernel on model
parameters. All these results are obtained for Kato decomposable electrostatic
potentials and the actual assumptions on the model are general enough to cover
the Nelson model as well. As a corollary we obtain some new pointwise
exponential decay and continuity results on elements of low-energetic spectral
subspaces of atoms or molecules that also take spin into account. In a simpler
situation where spin is neglected we explain how to verify the joint continuity
of positive ground state eigenvectors with respect to spatial coordinates and
model parameters. There are no smallness assumptions imposed on any model
parameter.

13
The categories of this paper are: quant-ph
20
The categories of this paper are: acc-phys
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: stat
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The categories of this paper are: econ
5
The categories of this paper are: gr-qc