Abstract
The concept of dimensional reduction in the high temperature regime is generalized to static Green's functions of composite operators that contain fermionic fields. The recognition of a natural kinematic region where the lowest Matsubara modes are close to their mass-shell, and the ultraviolet behavior of the running coupling constant of the original theory are crucial for providing the necessary scale hierarchy. The general strategy is illustrated in the asymptotically-free Gross-Neveu model in 1 + 1 dimensions, where we verify that dimensional reduction occurs to the leading order in g 2( T). We also find, in the same model, that the scale parameter characterizing the dependence on temperature of the coupling constant in the reduced theory, Λ T , is considerably smaller than Λ MS . Implications of our results for QCD are also discussed.
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