Asymptotic freedom and the thermal Lee model

Dimensional regularization is used to investigate the renormalization of the fermionmass, wave function, and coupling constant in theV-sector of a thermal Leemodel in arbitrary space–time dimensionsD and temperatureT. A closed expression of the fermionmass renormalization shows that it diverges at the high-T limit and replicates a familiar format the zero-T limit.Corresponding expressions of thewave function renormalization and the renormalized coupling constant vanish at the high-T limit, and resume respective customary forms at the zero-T limit. Likewise, the intrinsic scattering amplitude vanishes at thehigh-T limit, and reduces to the original amplitude at the zero-T limit. The 1D theory is especially useful for schematically graphing expressions that show thermal effects on theprobability, the bare coupling constant, and thebaremass. Bifurcationof thebare parameters is a prominent feature in these graphs for particular choice of input. Theβ andγ coefficients of theCallan–Symanzik equation are calculated in closed form, and correlations between theβ coefficient and theprobability are in evidence for dimensions less than, or greater than4. Schematic graphs incorporatingLaurent expansions of theβ coefficient, the probability, and the fermion-mass show the dependency of these functions upon the physical parameters in the theory for specific values ofD. The thermalmodel is found to be asymptotically free forD<4, and for oddD…5 at the high-T limit.