Gaussian approximation to the condensation of the interacting Bose gas

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.