Abstract
The renormalization group for finite temperature quantum field theories is studied, in particular for λϕ4. It is shown that the “high” temperature limit can only be discussed perturbatively ifT dependent renormalization schemes are implemented. Zero temperature renormalization schemes or renormalization at some fixed reference temperatureTo are both inadequate as they imply perturbative expansions about fixed points of the renormalization group which are associated with a zero temperature system and a system at temperatureTo respectively.T dependent schemes give rise to an expansion about the true fixed point of the system, the resulting renormalization group allows the entire crossover between high and low temperature behaviour to be investigated.
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