  Long ago Coleman, Callan, Wess and Zumino (CCWZ) constructed the general
effective lagrangian for nonlinearly realized symmetry by finding all possible
nonlinear representations of the broken group G which become linear when
restricted to the unbroken group H. However, in the case of a single
Nambu-Goldstone boson (NGB), which corresponds to a broken U(1), the effective
lagrangian can also be obtained by imposing a constant shift symmetry. In this
work we generalize the shift symmetry approach to multiple NGBs and show that,
when they furnish a linear representation of H that can be embedded in a
symmetric coset, it is possible to derive the CCWZ lagrangian by imposing 1)
the "Adler's zero condition," which requires scattering amplitudes to vanish
when emitting a single soft NGB, and 2) closure of shift symmetry with the
linearly realized symmetry; knowledge of the broken group G is not required at
all. Using only generators of H, the NGB covariant derivative and the
associated gauge field can be computed to all orders in the NGB decay constant
f.
