A Guide to Localized Frames and Applications to Galerkin-like Representations of Operators

This chapter offers a detailed survey on intrinsically localized frames and the corresponding matrix representation of operators. We re-investigate the properties of localized frames and the associated Banach spaces in full detail. We investigate the representation of operators using localized frames in a Galerkin-type scheme. We show how the boundedness and the invertibility of matrices and operators are linked and give some sufficient and necessary conditions for the boundedness of operators between the associated Banach spaces.Comment: 32 page

The HERA polarimeter and the first observation of electron spin polarization at HERA

Available from TIB Hannover: RA 2999(92-136) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Tests of Classical and Quantum Electrodynamics with Intense Laser Fields

n this chapter classical and quantum electrodynamics in intense laser fields are discussed. We focus on the interaction of relativistic electrons with strong laser pulses. In particular, by analyzing the dynamics of this interaction, we show how the peak intensity of a strong laser pulse can be related to the spectrum of the radiation emitted by the electron during the interaction itself. The discussed method could be used to accurately measure high peak laser intensities exceeding 1020 W/cm2 up to about 1023 W/cm2 with theoretical envisaged accuracies of the order of 10 %. Furthermore, we investigate non-linear quantum effects originating from the interaction of an electron with its own electromagnetic field in the presence of an intense plane wave. These “radiative corrections” modify the electron wave-function in the plane wave. The self-interaction changes, amongst others, the dynamics of the electron’s spin in comparison with the prediction of the Dirac equation. We show that this effect can be measured, in principle, already at intensities of the order of 1022 W/cm