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A modified perturbation scheme is set up for a scalar field theory at finite temperature. Here the mass term is replaced by an effective mass, to be determined by calculating the two-point function at zero momentum. Using the real-time formulation we calculate the latter to second order in this modified scheme. The result is used to calculate the critical temperature in a Higgs model to the same order.
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Banerjee et al. (1991) studied this question.
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