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Conference on "Variational and spectral methods in Quantum Field Theory"
Organizers: Volker Bach (Braunschweig), Maria J. Esteban (CNRS), Mathieu Lewin (CNRS), Eric Séré (Paris-Dauphine)


Sébastien Breteaux (Braunschweig, Germany): "Minimisation of the energy of an electron interacting with a photon field for quasifree states"
Thursday 25 April 2013, 16:15 - 17:00
Amphi Hermite


We introduce the non-relativistic Pauli-Fierz model for an electron interacting with a photon field. To obtain an upper bound on the ground state energy a good strategy is to compute the minimum of the energy on a subclass of states where the computations are simpler. We introduce two such classes of states, coherent states and quasifree states. We present the energy functionals in terms of parameters describing the coherent/quasifree states. We prove under some hypotheses:
  - the existence and uniqueness of a minimizer for these functionals,
  - how to get an expansion of the energy at this minimizer in terms of
the coupling constant appearing in the Pauli-Fierz model and of the total momentum.

Based on joint work with Volker Bach and Timmy Tzaneteas.