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SUMMARY:The mass shell in the semi-relativistic Pauli-Fierz model - Matte\
 , O (Aarhus Universitet)
DTSTART:20120803T100000Z
DTEND:20120803T104500Z
UID:TALK39167@talks.cam.ac.uk
CONTACT:Mustapha Amrani
DESCRIPTION:We consider the semi-relativistic Pauli-Fierz model for a sing
 le free electron interacting with the quantized radiation field. By transl
 ation invariance the corresponding Hamiltonian can be written as a direct 
 fiber integral with respect to different values of the total momentum of t
 he system. Employing a variant of Pizzo's iterative analytic perturbation 
 theory we prove that the mass shell\, i.e. the ground state energies of th
 e fiber Hamiltonians considered as a function of the total momentum\, is t
 wice continuously differentiable and strictly convex on balls about the or
 igin. The ground state energy at total momentum zero turns out to be an ei
 genvalue of the corresponding fiber Hamiltonian while there are no ground 
 state eigenvalues at non-vanishing total momenta. These results hold true\
 , for sufficiently small coupling constants depending on an ultraviolet cu
 toff and the radii of the balls. \n\nThe talk is based on joint work with 
 Martin Koenenberg (Vienna).\n\n
LOCATION:Seminar Room 1\, Newton Institute
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