  It is shown that a true Nambu-Goldstone (NG) boson develops a coherent
long-range field whenever the charge associated with it that is carried by the
other particles is not conserved in a macroscopic scale. The source of a NG
field is the time rate of quantum number violation. If the lepton numbers are
spontaneously broken at a scale below 1 TeV, the neutrino oscillation processes
generate long-range majoron fields that are strong enough in Supernovae to
modify the neutrino flavor dynamics. Two examples are given: NG fields may
improve the adiabaticity of $\nu_{e}\leftrightarrow \nu_{X}$ transitions or
cause resonant anti-neutrino oscillations otherwise impossible with solely weak
interactions.
