The RPA correlations in the presence of thermal fluctuations

We investigate the RPA correlations at finite temperature in the presence of thermal fluctuations in the context of the microscopic static path approximation. The RPA correction to the partition function is evaluated exactly. Its effects for the case of discrete and continuous broken symmetries in the mean field are then examined in a solvable model. The Goldstone modes and the treatment of repulsive terms in the interaction are also discussed.