12 research outputs found
The mass shell in the semi-relativistic Pauli-Fierz model
We consider the semi-relativistic Pauli-Fierz model for a single free
electron interacting with the quantized radiation field. Employing a variant of
Pizzo's iterative analytic perturbation theory we construct a sequence of
ground state eigenprojections of infra-red cutoff, dressing transformed fiber
Hamiltonians and prove its convergence, as the cutoff goes to zero. Its limit
is the ground state eigenprojection of a certain Hamiltonian unitarily
equivalent to a renormalized fiber Hamiltonian acting in a coherent state
representation space. The ground state energy is an exactly two-fold degenerate
eigenvalue of the renormalized Hamiltonian, while it is not an eigenvalue of
the original fiber Hamiltonian unless the total momentum is zero. These results
hold true, for total momenta inside a ball about zero of arbitrary radius p>0,
provided that the coupling constant is sufficiently small depending on p and
the ultra-violet cutoff. Along the way we prove twice continuous
differentiability and strict convexity of the ground state energy as a function
of the total momentum inside that ball.Comment: 44 page