We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter ...

In the first part of this note an elementary proof is given of the fact that algebraic functors, that is, functors induced by morphisms of Lawvere theories, have left adjoints provided that the category K in which the models of these theories take their values is locally presentable. The main focus however lies on the special cases of the underlying functor of the category Grp(K) of internal gr...

Given a normal (multi-)modal logic Θ, a characterization is given of the finitely presentable algebras A whose logics LA split the lattice of normal extensions of Θ. This is a substantial generalization of [Rautenberg, 1980; Rautenberg, 1977] in which Θ is assumed to be weakly transitive and A to be finite. We also obtain as a direct consequence a result by [Blok, 1978] that for all cycle-free ...

We show that subobjects and quotients respectively of any object K in a locally finitely presentable category form an algebraic lattice. The same holds for the internal equivalence relations on K. In fact, these results turn out to be—at least in the case of subobjects—nothing but simple consequences of well known closure properties of the classes of locally finitely presentable categories and ...

The rst challenge in robustness analysis of large-scale interconnected uncertain systems is to provide a model of such systems in a standardform that is required within di erent analysis frameworks. This becomes particularly important for large-scale systems, as analysis tools that can handle such systems heavily rely on the special structure within such model descriptions. We here propose an a...

We extend our previous theory of the gauging of classical quadratically nonlinear algebras without a central charge but with a coset structure, to the quantum level. Inserting the minimal anomalies into the classical transformation rules of the currents introduces further quantum corrections to the classical transformation rules of the gauge fields and currents which additively renormalize the ...

In this paper, we discuss the role of an external magnetic field on the dynamically generated fermion mass in even-flavor QED in three space-time dimensions. Based on some reasonable approximations, we present analytic arguments on the fact that, for weak fields, the magnetically-induced mass increases quadratically with increasing field, while at strong fields one crosses over to a mass scalin...