TY - JOUR

T1 - A note on polarization vectors in quantum electrodynamics

AU - Lieb, Elliott H.

AU - Loss, Michael

N1 - Copyright:
Copyright 2005 Elsevier B.V., All rights reserved.

PY - 2004/12

Y1 - 2004/12

N2 - 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.

AB - 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.

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U2 - 10.1007/s00220-004-1185-5

DO - 10.1007/s00220-004-1185-5

M3 - Article

AN - SCOPUS:11244264569

VL - 252

SP - 477

EP - 483

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 1-3

ER -