\noindent{\bf Mathematisches Oberseminar} {\it PDG und
Spektraltheorie} (WiSe 2013/14).

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\noindent{\bf Date:} 05.12.2013.

\noindent{\bf Time and place:} 14:15 in B 134.

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\noindent{\bf Speaker:} Oliver Matte (Aarhus University \& LMU).

\noindent{\bf Titel:} {\it Stochastic differential equations
associated with the standard model of nonrelativistic quantum
electrodynamics}. 


\noindent{\bf Abstract:}

\noindent 
The standard model of nonrelativistic quantum electrodynamics
describes quantum mechanical matter particles (electrons) interacting
with a quantized radiation field (photon field). 
The corresponding Hamiltonian can be considered as a Schr\"{o}dinger
operator for the matter particles perturbed by certain non-commuting
operators acting in a bosonic Fock space. We derive and discuss
stochastic differential equations associated with the heat semi-group
of this model . In particular, we re-derive Feynman-Kac type formulas
for spinless matter particles and obtain new Feynman-Kac formulas
involving series of time-ordered integrals of certain
annihilation-preservation-creation processes when the electron spin is
taken into account. Moreover, we discuss stochastic differential
equations and Feynman-Kac representations for an operator-valued
integral kernel of the semi-group. Applications to the study of
regularity properties of the semi-group and its integral kernel will
be mentioned. 

\noindent The talk is based on joint work with Batu G\"{u}neysu and Jacob Schach
M{\o}ller.  


\noindent 

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Thomas {\O}stergaard S{\o}rensen

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