  The Schwinger boson theory provides a natural path for treating quantum spin
systems with large quantum fluctuations. In contrast to semi-classical
treatments, this theory allows us to describe a continuous transition between
magnetically ordered and spin liquid states, as well as the continuous
evolution of the corresponding excitation spectrum. The square lattice
Heisenberg antiferromagnet is one of the first models that was approached with
the Schwinger boson theory. Here we revisit this problem to reveal several
subtle points that were omitted in previous treatments and that are crucial to
further develop this formalism. These points include the freedom for the choice
of the saddle point (Hubbard-Stratonovich decoupling and choice of the
condensate) and the $1/N$ expansion in the presence of a condensate. A key
observation is that the spinon condensate leads to Feynman diagrams that
include contributions of different order in $1/N$, which must be accounted to
get a qualitatively correct excitation spectrum. We demonstrate that a proper
treatment of these contributions leads to an exact cancellation of the
single-spinon poles of the dynamical spin structure factor, as expected for a
magnetically ordered state. The only surviving poles are the ones arising from
the magnons (two-spinon bound states), which are the true collective modes of
an ordered magnet.
