We examine the general issue of whether a scale dependent cosmological constant can be consistent with general covariance, a problem that arises naturally in the treatment of quantum gravitation, where coupling constants generally run as a consequence of renormalization group effects. The issue is approached from several points of view, which include the manifestly covariant functional integral formulation, covariant continuum perturbation theory about two dimensions, the lattice formulation of gravity, and the nonlocal effective action and effective field equation methods. In all cases we find that the cosmological constant cannot run with scale, unless general covariance is explicitly broken by the regularization procedure. Our results are expected to have some bearing on current quantum gravity calculations, but more generally should apply to phenomenological approaches to the cosmological vacuum energy problem. © 2013 World Scientific Publishing Company.

In some models of electroweak interactions the W and Z bosons are considered composites, made up of spin-$\frac12$ subconstituents. In these models a spin-0 counterpart of the W and Z boson naturally appears, whose higher mass can be attributed to a particular type of hyperfine spin interaction among the various subconstituents. Recently, it has been argued that the scalar state could be identified with the newly discovered Higgs (H) candidate. Here, we use the known spin splitting between the W/Z and H states to infer, within the framework of a purely phenomenological model, the relative strength of the spin-spin interactions. The results are then applied to the lepton sector, and used to crudely estimate the relevant spin splitting between the two lowest states. Our calculations in many ways parallels what is done in the SU(6) quark model, where most of the spin splittings between the lowest lying baryon and meson states are reasonably well-accounted for a simple color hyperfine interaction, with constituent (color-dressed) quark masses. © 2014 World Scientific Publishing Company.

Physical properties of the quantum gravitational vacuum state are explored by solving a lattice version of the Wheeler-DeWitt equation. The constraint of diffeomorphism invariance is strong enough to uniquely determine part of the structure of the vacuum wave functional in the limit of infinitely fine triangulations of the three-sphere. In the large fluctuation regime, the nature of the wave function solution is such that a physically acceptable ground state emerges, with a finite nonperturbative correlation length naturally cutting off any infrared divergences. The location of the critical point in Newton's constant Gc, separating the weak from the strong coupling phase, is obtained, and it is inferred from the general structure of the wave functional that fluctuations in the curvatures become unbounded at this point. Investigations of the vacuum wave functional further suggest that for weak enough coupling, G