Abstract
At low temperatures and large volumes, the partition function is dominated by the Goldstone bosons generated by spontaneous symmetry breakdown. We show that the behaviour of the system can be analyzed in terms of an effective lagrangian, whose coupling constants are independent of the temperature, but, in general, depend on the volume. If the Bose (Fermi) fields of the underlying theory are subject to periodic (antiperiodic) boundary conditions, there is no volume dependence: the effective lagrangian coincides with the standard, Lorentz invariant expression which describes the behaviour of the system at infinite volume and at zero temperature.
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