Vacuum polarization in a static uniform electromagnetic field with applications to pulsars

Relativistic quantum theory and plasma theory are extended and combined in this thesis. Specific response tensors (for a plasma) and vacuum polarization tensors are calculated and plasma techniques are used to treat certain relativistic quantum processes in the presence of a static uniform electromagnetic field. The linear vacuum polarization tensor in an electromagnetic wrench (i.e. in parallel electric and magnetic fields) is calculated exactly as a function of the field strengths and the wave vector. The tensor is renormalized explicitly by a consideration of its tensor structure. The wave properties and absorption coefficients (due to pair production) for the two electromagnetic modes of the birefringent vacuum are calculated exactly. The conditions for Cerenkov emission in the vacuum permeated by an electromagnetic wrench are investigated. An alternative method for calculating the linear vacuum polarization tensor in a magnetic field is developed using the relation between the imaginary part of the tensor and the probability for emission and absorption of a photon by an electron in a magnetic field. For a spatially dispersive medium the requirements of causality and special relativity are used to develop a generalized dispersion relation (a generalization of the Kramers-Krönig dispersion relation). An error is pointed out in earlier versions of this relation. The field-free linear vacuum polarization tensor is shown to satisfy the generalized dispersion relation explicitly. The quadratic vacuum polarization tensor in a magnetic field is calculated exactly as a function of the field strength and the wave vectors. The tensor is used to derive exact absorption coefficients due to photon splitting in the magnetized vacuum, including the effects of the magnetic field on the properties of the photons. The properties of the natural wave modes of a relativisticallystreaming electron-positron plasma in an intense magnetic field are explored. The results are applied to an interpretation of the polarization characteristics of pulsar radio emission. The wave properties for the optical, X-ray and y-ray emissions from the near magnetosphere of a pulsar are shown to be determined by the polarization of the magnetized vacuum. It is established that Cerenkov emission and photon splitting in the magnetized vacuum are insignificant in a pulsar magnetosphere