Spontaneous breakdown in quantum electrodynamics

On higher-spin supertranslations and superrotations

“…Our construction is based on the definition of a suitable Bondi-like gauge for higher spins, whose consistency is further discussed in section 4. In section 5 we take a different perspective and consider the possibility to derive Weinberg's result for any spin as the Goldstone theorem of a specific class of large gauge transformations, thus extending the results of [20,21]. This approach provides a non-perturbative result that allows in principle to keep track also of the subleading corrections.…”

“…One can extend the usual proof of Goldstone's theorem [21,33] by using the fact that the non-covariant piece of (5.6) involves the generator j µν = h µν of the (unbroken) global symmetry. According to the Goldstone theorem, if the symmetry is broken then there are massless one-particle modes in the Fourier transform of 0|δ (l) B|0 , where B is the order parameter.…”

“…The photon itself was then reinterpreted as the associated Goldstone particle. In this section we generalise the strategy of [20,21] to all spins. In particular we detail the case of linearised gravity, since the higher-spin case obtains by the latter in a straightforward manner, as we sketch at the end of the section.…”

“…In two pioneering papers by Ferrari and Picasso [20,21], Weinberg's soft photon theorem [2] and its subleading corrections [29][30][31] were shown to follow from the Goldstone theorem applied to the breaking of a suitable class of "large gauge symmetries" of QED, namely those with linear gauge parameters. The photon itself was then reinterpreted as the associated Goldstone particle.…”

“…Limiting ourselves to the main formulae, the Ward identity linking the matter propagator S(p) to the s-field vertex function Γ µ 1 ...µs reads 21) and the soft theorem expressing the amputated amplitude K µ 1 ...µs (p, p , q) for the process K(p, p , q) with the addition of an extra soft spin-s particle with momentum k µ is encoded in the following expression,…”