Journal of High Energy Physics

, 2014:112 | Cite as

New symmetries of massless QED

  • Temple He
  • Prahar Mitra
  • Achilleas P. PorfyriadisEmail author
  • Andrew Strominger
Open Access


An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function \( \varepsilon \left(z,\overline{z}\right) \) on the conformal sphere at future null infinity ( Open image in new window ) but are independent of the retarded time. The value of ε at past null infinity ( Open image in new window ) is determined from that on Open image in new window by the condition that it take the same value at either end of any light ray crossing Minkowski space. The ε ≠ constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.


Spontaneous Symmetry Breaking Scattering Amplitudes Gauge Symmetry 


Open Access

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Copyright information

© The Author(s) 2014

Authors and Affiliations

  • Temple He
    • 1
  • Prahar Mitra
    • 1
  • Achilleas P. Porfyriadis
    • 1
    Email author
  • Andrew Strominger
    • 1
  1. 1.Center for the Fundamental Laws of NatureHarvard UniversityCambridgeUnited Kingdom

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