Electroweak Higgs potentials and vacuum stability

In electroweak models, radiative corrections to the scalar potential can have significant consequences. In the standard model, they can destabilize the standard model vacuum; the requirement of vacuum stability leads to severe bounds on Higgs and fermion masses. In supersymmetric models, they lead to the generation of the electroweak scale in terms of the unification scale. In this report, the method of calculating radiative corrections to the scalar potential is reviewed, with an emphasis on renormalization group improvement of the potential. Finite temperature corrections to the potential, calculation of tunnelling rates and the nature of cosmological phase transitions are then discussed, and the results are then applied to the standard model to derrive stringent bounds on Higgs and fermion passes. These results are then generalized to models with several Higgs fields. Finally, the scalar potential in supersymmetric models, including dimensional transmutation and no-scale models, is discussed. (orig.) With 465 refs