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Antisymmetric tensor fields interacting with quarks and leptons have been proposed as a possible solution to the gauge hierarchy problem. We compute the one-loop beta function for a quartic self-interaction of the chiral antisymmetric tensor fields. Fluctuations of the top quark drive the corresponding running coupling to a negative value as the renormalization scale is lowered. This may indicate a non-vanishing expectation value of the tensor field, and thus a spontaneous breaking of Lorentz invariance. Settling this issue will need the inclusion of tensor loops., Comment: 15 pages, 4 figures

A second rank antisymmetric tensor field is proposed as an alternative to the Higgs scalar. No mass term is allowed by the symmetries. At the scale where the asymptotically free chiral couplings of the fermions grow large, condensates of top-antitop and bottom-antibottom may induce the spontaneous breaking of the electroweak gauge symmetry. This would solve the gauge hierarchy problem by dimensional transmutation, similar to QCD., Comment: extended discussion of consistency and mass generation, 4 pages

The critical behaviour of a system of two coupled scalar fields in three dimensions is studied within the formalism of the effective average action. The fixed points of the system are identified and the crossover between them is described in detail. Besides the universal critical behaviour, the flow of the coarse grained free energy also describes the approach to scaling., Comment: 18 pages, latex, 4 figures appended as uuencoded file

We perform a non-perturbative study of the Coleman-Weinberg phase transition in scalar QED. Our method permits a consistent treatment of the effective potential near the origin, a region not accessible to perturbation theory. As a result, we establish reliably the first order character of the phase transition for arbitrary values of the scalar coupling., Comment: 17 pages, 4 figures added in PostScript, HD-THEP-94-23, OUTP-94-12

We derive exact equations describing the dependence of the average action on the scale k characteristic for the averaging. Such an equation is a differential equation with infinitely many variables. We reformulate it as a system of infinitely many differential equations for infinitely many couplings and sketch systematic expansions for this system. We also establish the connection between these equations and other formulations of exact renormalization group equations.