A note on polarization vectors in quantum electrodynamics

Elliott H. Lieb, Michael Loss

Research output: Contribution to journalArticlepeer-review

22 Scopus citations


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 ελ (k) with λ ∈ {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.

Original languageEnglish (US)
Pages (from-to)477-483
Number of pages7
JournalCommunications In Mathematical Physics
Issue number1-3
StatePublished - Dec 2004

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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