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arXiv · 1407.3789

New Symmetries of Massless QED

Temple He·Prahar Mitra·Achilleas P. Porfyriadis·Andrew Strominger
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Abstract

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 $\varepsilon(z,\bar{z})$ on the conformal sphere at future null infinity ($\mathscr I^+$) but are independent of the retarded time. The value of $\varepsilon$ at past null infinity ($\mathscr I^-$) is determined from that on $\mathscr I^+$ by the condition that it take the same value at either end of any light ray crossing Minkowski space. The $\varepsilon\neq$ 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.

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Temple He, Prahar Mitra, Achilleas P. Porfyriadis, Andrew Strominger. 2016-02-09. New Symmetries of Massless QED. https://doi.org/10.1007/jhep10(2014)112

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