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Our purpose in this paper is to explore the properties of the natural wave modes of a relativistically streaming electron-positron gas and to apply the results to the interpretation of the polarization characteristics of pulsar radio emission.

Abstract. The exact vacuum polarization 4-tensor in the presence of a static magnetic field is calculated by a method due to Svetozarova and Tsytovich. The Hermitian part of the tensor is explicitly renormalized by Shabad's diagonalization with respect to tensor indices and the anti-Hermitian part of the tensor is found to be finite and gauge invariant. An alternative method for calculating the vacuum polarization tensor is developed using the relation between the anti-Hermitian part of the tensor and the probability of emission and absorption of a photon by an electron in a static magnetic field.

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