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A Note on Polarization Vectors in Quantum Electrodynamics

Elliott H. Lieb·Michael Loss
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Abstract

A photon of momentum k can have only two polarization states, not three. Equivalently, one can say that the magnetic vector potential A must be divergence free in the Coulomb gauge. These facts are normally taken into account in QED by introducing two polarization vectors epsilon_λ(k) with lambda in {1,2}, which are orthogonal to the wave-vector k. These vectors must be very discontinuous functions of k and, consequently, their Fourier transforms have bad decay properties. Since these vectors have no physical significance there must be a way to eliminate them and their bad decay properties from the theory. We propose such a way here.

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Elliott H. Lieb, Michael Loss. 2004-01-08. A Note on Polarization Vectors in Quantum Electrodynamics. https://doi.org/10.1007/s00220-004-1185-5

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