999 research outputs found
A Note on Polarization Vectors in Quantum Electrodynamics
A photon of momentum k can have only two polarization states, not three.
Equivalently, one can say that the magnetic vector potential A must be
divergence free in the Coulomb gauge. These facts are normally taken into
account in QED by introducing two polarization vectors epsilon_\lambda(k) with
lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must
be very discontinuous functions of k and, consequently, their Fourier
transforms have bad decay properties. Since these vectors have no physical
significance there must be a way to eliminate them and their bad decay
properties from the theory. We propose such a way here.Comment: 6 pages late
Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation
For a large class of quantum mechanical models of matter and radiation we
develop an analytic perturbation theory for non-degenerate ground states. This
theory is applicable, for example, to models of matter with static nuclei and
non-relativistic electrons that are coupled to the UV-cutoff quantized
radiation field in the dipole approximation. If the lowest point of the energy
spectrum is a non-degenerate eigenvalue of the Hamiltonian, we show that this
eigenvalue is an analytic function of the nuclear coordinates and of
, being the fine structure constant. A suitably chosen
ground state vector depends analytically on and it is twice
continuously differentiable with respect to the nuclear coordinates.Comment: 47 page
On the Smooth Feshbach-Schur Map
A new variant of the Feshbach map, called smooth Feshbach map, has been
introduced recently by Bach et al., in connection with the renormalization
analysis of non-relativistic quantum electrodynamics. We analyze and clarify
its algebraic and analytic properties, and we generalize it to non-selfadjoint
partition operators and \chib.Comment: 8 page
- …