Dynamical symmetry breaking and the renormalization group

Renormalization-group techniques are applied to determine under what conditions massless field theories can dynamically generate a mass. The conjecture that infrared-stable field theories cannot generate a mass is verified, and necessary conditions for mass generation at nontrivial fixed points are derived. The Schwinger model in $n$ dimensions is studied, and it is shown that dynamical symmetry breaking is very likely unique to $n=2\mathrm{}$, for the Abelian theory. These techniques are used to examine the possible dynamical nature of lepton masses, and several previously studied models exhibiting dynamical symmetry breaking are reexamined using renormalization-group methods.