6533b832fe1ef96bd129af78
RESEARCH PRODUCT
Construction of the ground state in nonrelativistic QED by continuous flows
Martin KönenbergVolker Bachsubject
PhysicsIntegrable systemQEDApplied MathematicsGround stateOdeAtom (order theory)Spectral analysisRenormalization groupProjection (linear algebra)Fundamental theorem of calculusQuantum mechanicsLimit (mathematics)Ground stateRenormalization groupAnalysisdescription
AbstractFor a nonrelativistic hydrogen atom minimally coupled to the quantized radiation field we construct the ground state projection Pgs by a continuous approximation scheme as an alternative to the iteration scheme recently used by Fröhlich, Pizzo, and the first author [V. Bach, J. Fröhlich, 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 Pgs=limt→∞Pt as the limit of a continuously differentiable family (Pt)t⩾0 of ground state projections of infrared regularized Hamiltonians Ht. Using the ODE solved by this family of projections, we show that the norm ‖P˙t‖ of their derivative is integrable in t which in turn yields the convergence of Pt by the fundamental theorem of calculus.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2006-12-01 | Journal of Differential Equations |