Construction of the ground state in nonrelativistic QED by continuous flows

[摘要] 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 Frohlich, Pizzo, and the first author [V. Bach, J. Frohlich, A. Pizzo, Infrared-finite algorithms in QED: The groundstate of an atom interacting with the quantized radiation field, Comm. Math. Phys. (2006), doi: 10. 1007/s00220-005-1478-3]. That is, we construct P-gs = lim(t ->infinity) P-t as the limit of a continuously differentiable family (P-t)(t >= 0) of ground state projections of infrared regularized Hamiltomans H-t. Using the ODE solved by this family of projections, we show that the norm parallel to<(P)over dot>(t)parallel to of their derivative is integrable in t which in turn yields the convergence of Pt by the fundamental theorem of calculus. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-15

[关键词] QED;spectral analysis;renormalization group;ground state