Inner products of resonance solutions in 1-D quantum barriers

The properties of a prescription for the inner products of the resonance (Gamow states), scattering (Dirac kets), and bound states for 1-dimensional quantum barriers are worked out. The divergent asypmtotic behaviour of the Gamow states is regularized using a Gaussian convergence factor first introduced by Zel'dovich. With this prescription, most of these states (with discrete complex energies) are found to be orthogonal to each other, to the bound states, and to the Dirac kets, except when they are neighbors, in which case the inner product is divergent. Therefore, as it happens for the continuum scattering states, the norm of the resonant ones remains non-calculable. Thus, they exhibit properties half way between the (continuum real) Dirac-delta orthogonality and the (discrete real) Kronecker-delta orthogonality of the bound states.Comment: 13 pages, 2 figure

Dynamical variables in Gauge-Translational Gravity

Assuming that the natural gauge group of gravity is given by the group of isometries of a given space, for a maximally symmetric space we derive a model in which gravity is essentially a gauge theory of translations. Starting from first principles we verify that a nonlinear realization of the symmetry provides the general structure of this gauge theory, leading to a simple choice of dynamical variables of the gravity field corresponding, at first order, to a diagonal matrix, whereas the non-diagonal elements contribute only to higher orders.Comment: 15 page

Non-Linear Affine Embedding of the Dirac Field from the Multiplicity-Free SL(4,R) Unirreps

The correspondence between the linear multiplicity-free unirreps of SL(4, R) studied by Ne'eman and {\~{S}}ija{\~{c}}ki and the non-linear realizations of the affine group is worked out. The results obtained clarify the inclusion of spinorial fields in a non-linear affine gauge theory of gravitation.Comment: 13 pages, plain TeX, macros include

Gravitational contribution to fermion masses

In the context of a nonlinear gauge theory of the Poincar\'e group, we show that covariant derivatives of Dirac fields include a coupling to the translational connections, manifesting itself in the matter action as a universal background mass contribution to fermions.Comment: revtex4, 9 pages, no figures, to be published in Eur.Phys.J.C, 200

Holographic bounds and Higgs inflation

In a recently proposed scenario for primordial inflation, where the Standard Model (SM) Higgs boson plays a role of the inflation field, an effective field theory (EFT) approach is the most convenient for working out the consequences of breaking of perturbative unitarity, caused by the strong coupling of the Higgs field to the Ricci scalar. The domain of validity of the EFT approach is given by the ultraviolet (UV) cutoff, which, roughly speaking, should always exceed the Hubble parameter in the course of inflation. On the other hand, applying the trusted principles of quantum gravity to a local EFT demands that it should only be used to describe states in a region larger than their corresponding Schwarschild radius, manifesting thus a sort of UV/IR correspondence. We consider both constraints on EFT, to ascertain which models of the SM Higgs inflation are able to simultaneously comply with them. We also show that if the gravitational coupling evolves with the scale factor, the holographic constraint can be alleviated significantly with minimal set of canonical assumptions, by forcing the said coupling to be asymptotically free.Comment: 9 pages, new material and references added, to appear in PL

Newtonian Limit of Conformal Gravity

We study the weak-field limit of the static spherically symmetric solution of the locally conformally invariant theory advocated in the recent past by Mannheim and Kazanas as an alternative to Einstein's General Relativity. In contrast with the previous works, we consider the physically relevant case where the scalar field that breaks conformal symmetry and generates fermion masses is nonzero. In the physical gauge, in which this scalar field is constant in space-time, the solution reproduces the weak-field limit of the Schwarzschild--(anti)DeSitter solution modified by an additional term that, depending on the sign of the Weyl term in the action, is either oscillatory or exponential as a function of the radial distance. Such behavior reflects the presence of, correspondingly, either a tachion or a massive ghost in the spectrum, which is a serious drawback of the theory under discussion.Comment: 9 pages, comments and references added; the version to be published in Phys. Rev.

Average Effective Potential for the Conformal Factor

In a four dimensional theory of gravity with lagrangian quadratic in curvature and torsion, we compute the effective action for metrics of the form $g_{\mu\nu}=\rho^2\delta_{\mu\nu}$, with $\rho$ constant. Using standard field-theoretic methods we find that one loop quantum effects produce a nontrivial effective potential for $\rho$. We explain this unexpected result by showing how our regularization procedure differs from the one that is usually adopted in Quantum Gravity. Using the method of the average effective potential, we compute the scale dependence of the v.e.v. of the conformal factor.Comment: 8 pages, plain TEX, SISSA 71/93-E