  The effective action formalism of quantum field theory is used to study the
properties of the non-relativistic interacting Bose gas. The Gaussian
approximation is formulated by calculating the effective action to the first
order of the optimized expansion. In the homogeneous limit the method respects
the Hughenholz-Pines theorem, leading to the gapless spectrum both for
excitations and for density fluctuations. Renormalization is carried out by
adopting dimensional regularization. The results for critical temperature are
compared with that obtained in the loop expansion.
