Abstract
Propagation of photons (or of any spin-1 boson) is of interest in different kinds of non-trivial background, including a thermal bath, or a background magnetic field, or both. We give a unified treatment of all such cases, casting the problem as a matrix eigenvalue problem. The matrix in question is not a normal matrix, and therefore care should be given to distinguish the right eigenvectors from the left eigenvectors. The polarization vectors are shown to be right eigenvectors of this matrix, and the polarization sum formula is seen as the completeness relation of the eigenvectors. We show how this method is successfully applied to different non-trivial backgrounds.
Highlights
Propagation of electromagnetic waves through any background is a subject of huge interest
In the language of quantum theory, we rename this subject as the question of photon propagation
Using the methods of quantum field theory in thermal background, the question of photon propagation was analyzed in a thermal background [1,2], and well-known attributes of material medium like the dielectric constant and the magnetic permeability were identified in the framework of the quantum field theoretical treatment
Summary
Propagation of electromagnetic waves through any background is a subject of huge interest. The more general case of a magnetic field in a medium, combining the two kinds of backgrounds mentioned earlier, has been a subject of great interest [4,7]. In many cases the discussion does not explicitly mention photons, but rather gluons [8,9,10] or even ρ-mesons [11], but that makes no difference in the general structure of the problem It is the problem of the propagation of a spin-1 boson in a nontrivial background. What we propose to do in this paper is to develop a unified approach that works for all kinds of background. Important insight into the question of photon propagation, which we will apply to specific backgrounds, rediscovering some of the old formulas with the new insight, and finding expressions for the polarization vectors which are sometimes difficult to find from the usual approach
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