Bach V., Koenenberg M.
Construction of the Ground State in Nonrelativistic QED by Continuous Flows
(333K, Postscript)
ABSTRACT. For a nonrelativistic hydrogen atom minimally coupled to the
quantized radiation field we construct the ground state projection
$P_\gs$ by a continuous approximation scheme as an alternative to the iteration scheme recently used by Froehlich, Pizzo, and the first author. That is, we construct $P_\gs =\lim_{t \to \infty} P_t$
as the limit of a continuously differentiable family $(P_t)_{t \geq 0}$ of ground state projections of infrared regularized Hamiltonians $H_t$. Using the ODE solved by this family of projections, we show that the norm $\| \dot{P}_t \|$ of their derivative is integrable in $t$ which in turn yields the convergence of $P_t$ by the fundamental theorem of calculus.