Infrared renormalization and infraparticle states in QED

Thomas Chen Courant Institute, NYU

We consider a freely propagating, non-relativistic, charged particle interacting with the quantized, ultraviolet regularized electromagnetic field. Introducing an infrared regularization σ_{0}, we study H_{p}(σ_{0}), the restriction of the corresponding hamiltonian to the fiber Hilbert space H_{p} associated to the conserved total momentum p. For |p| sufficiently small, we show that E_{0}(|p|, σ_{0}) =infspec(H_{p}(σ_{0})) is an eigenvalue, and that E_{0}(|p|, σ_{0}) − \frac{|p|^{2}}{2} has small first and second derivatives w.r.t. |p|, uniformly in σ_{0}. Furthermore, the corresponding eigenvector is an element of H_{p}(σ_{0}) for all σ_{0} > 0, but not in the limit σ_{0} → 0. The proof is based on the Bach-Fröhlich-Sigal operator-theoretic renormalization group.