The theory of quantum electrodynamics (QED) was born out of an attempt to merge Einsteins theory of special relativity and quantum mechanics. Einsteins energy/mass equivalence together with Heisenberg's uncertainty principle allows for particle pairs to be spontaneously created and annihilated in vacuum. These spontaneous fluctuations gives the quantum vacuum properties analogous to that of a nonlinear medium. Although these fluctuations in general does not give note of themselves, effects due to their presence can be stimulated or enhanced through external means, such as boundary conditions or electromagnetic fields. Whereas QED has been very well tested in the high-energy, low-intensity regime using particle accelerators, the opposite regime where the photon energy is low but instead the intensity is high is still to a large degree not investigated. This is expected to change with the rapid progress of modern high-power laser-systems. In this thesis we begin by studying the QED effect of photon-photon scattering. This process has so far not been successfully verified experimentally, but we show that this may change already with present day laser powers. We also study QED effects due to strong magnetic fields. In particular, we obtain an analytical description for vacuum birefringence valid at arbitrary field strengths. Astrophysics already offer environments where QED processes may be influential, e.g. in neutron star and magnetar environments. For astrophysical purposes we investigate how effects of QED can be implemented in plasma models. In particular, we study QED dispersive effects due to weak rapidly oscillating fields, nonlinear effects due to slowly varying strong fields, as well as QED effects in strongly magnetized plasmas. Effects of quantum dispersion and the electron spin has also been included in an extended plasma description, of particular interest for dense and/or strongly magnetized systems.

This thesis analyses the effect spin-orbit coupling has on the dispersion of Langmuir waves in magnetized plasmas, using recently developed kinetic theories of plasmas including quantummechanical and relativistic effects. Two new wave modes appearclose to the resonance <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5CDelta%20%5Comega_%7Bc%7D" /> = ( g/2 − 1)<img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Comega_%7Bc%7D" /> , where <img src="http://www.diva-portal.org/cgi-bin/mimetex.cgi?%5Comega_%7Bc%7D" /> is the cyclotron frequency and g is the electron gyromagnetic ratio. Forconsidered long wave lengths the deviation from this resonanceis very small. The wave modes are also very weakly damped.