Locally Equivalent Symmetries

The first obstacle to the application of the effective field theory program to spacetime symmetries is the identification of independent fluctuations of the order parameter. The redundancy among fluctuations induced by different broken symmetry generators often arises from the equivalence of the corresponding local symmetry transformations. This is explored in the present chapter. First, it is shown that symmetries that are locally equivalent give rise to closely related Noether currents. This explains how the Ward identities for the correlation functions of Noether currents can be saturated with a lower number of Nambu–Goldstone bosons than naively expected. The redundancy of different coordinate-dependent symmetries is then addressed from the point of view of background gauge invariance. The last part of the chapter returns to scattering of Nambu–Goldstone bosons. It shows how the presence of redundant symmetries may lead to the enhancement of scattering amplitudes in the soft limit.