Bose-Einstein condensation beyond perturbation theory: Goldstone singularities and instanton solution

Temperature Green functions are applied to the analysis of Bose-condensation of weakly interacting gas. The character of Goldstone singularities of correlation functions is established to all orders in perturbation theory. These singularities are regularized by the system volume. An anomalous volume dependence of the correlation functions is revealed. Quantum-field perturbation series are studied in the framework of the instanton approach. It is shown that there are no time-dependent instantons and that the time-independent instanton solutions exhibit factorial growth in large orders of the quantum-field perturbation expansion.