Equivalence in spin wave theories is pointed out from the viewpoint of
gauge invariance. Both the Holstein-Primakoff and the Dyson-Maleev re
presentations are derived by imposing certain gauge fixing conditions
on the Schwinger formalism which is gauge invariant. We show explicitl
y the equality of partition functions of the Heisenberg model calculat
ed in the Holstein-Primakoff and the Dyson-Maleev representations in h
igh-temperature expansion.