  A simple theorem is proved: When a gauge-invariant local field theory is
written in terms of matter fields alone, a composite gauge boson or bosons must
be formed dynamically. The theorem results from the fact that the Noether
current vanishes in such theories. The proof is carried out by use of the
charge-field algebra at equal time in the Heisenberg picture together with the
well-established analyticity of the form factor of the current. While there is
no need of diagram calculation for the proof, we demonstrate in the leading 1/N
expansion of the existing models what the theorem means in diagrams and how the
composite gauge boson emerges.
