Communications in Mathematical Physics

, Volume 252, Issue 1–3, pp 477–483 | Cite as

A Note on Polarization Vectors in Quantum Electrodynamics

  • Elliott H. Lieb
  • Michael Loss


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 ɛ λ (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.


Neural Network Fourier Fourier Transform Statistical Physic Complex System 
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Copyright information

© E.H. Lieb and M. Loss 2004

Authors and Affiliations

  • Elliott H. Lieb
    • 1
  • Michael Loss
    • 2
  1. 1.Departments of Physics and MathematicsJadwin Hall, Princeton UniversityPrincetonUSA
  2. 2.School of MathematicsGeorgia TechAtlantaUSA

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