The mass shell in the semi-relativistic Pauli-Fierz model
Friday 03 August 2012, 11:00-11:45
Seminar Room 1, Newton Institute
We consider the semi-relativistic Pauli-Fierz model for a single free electron interacting with the quantized radiation field. By translation invariance the corresponding Hamiltonian can be written as a direct fiber integral with respect to different values of the total momentum of the system. Employing a variant of Pizzo's iterative analytic perturbation theory we prove that the mass shell, i.e. the ground state energies of the fiber Hamiltonians considered as a function of the total momentum, is twice continuously differentiable and strictly convex on balls about the origin. The ground state energy at total momentum zero turns out to be an eigenvalue 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 cutoff and the radii of the balls.
The talk is based on joint work with Martin Koenenberg (Vienna).