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Comparison of two methods for calculating finite-temperature ring diagrams.

Certain types of ring diagrams of the thermodynamic potential {Omega} can be summed up to all orders using two apparently very different methods---the eigenvalue method and the transition-amplitude method. A relatively simple derivation of these methods is given, and we show that these two methods are exactly equivalent to each other. To study their numerical applications we have calculated the particle-particle, hole-hole ring diagrams of {Omega} for nuclear matter with both methods, using a modified Gogny interaction. Our results suggest that the strength-parameter integration involved in the transition-amplitude method can be accurately performed using a small number of mesh points and both methods seem to be suitable for numerical calculations.