Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stochastic differential equations for models of non-relativistic matter
  interacting with quantized radiation fields   We discuss Hilbert space-valued stochastic differential equations associated
with the heat semi-groups of the standard model of non-relativistic quantum
electrodynamics and of corresponding fiber Hamiltonians for translation
invariant systems. In particular, we prove the existence of a stochastic flow
satisfying the strong Markov property and the Feller property. To this end we
employ an explicit solution ansatz. In the matrix-valued case, i.e., if the
electron spin is taken into account, it is given by a series of operator-valued
time-ordered integrals, whose integrands are factorized into annihilation,
preservation, creation, and scalar parts. The Feynman-Kac formula implied by
these results is new in the matrix-valued case. Furthermore, we discuss
stochastic differential equations and Feynman-Kac representations for an
operator-valued integral kernel of the semi-group. As a byproduct we obtain
analogous results for Nelson's model.

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The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
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The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
31
The categories of this paper are: ao-sci