The phase of scalar field wormholes at one loop in the path integral formulation for Euclidean quantum gravity

We here calculate the one-loop approximation to the Euclidean Quantum Gravity coupled to a scalar field around the classical Carlini and Miji\'c wormhole solutions. The main result is that the Euclidean partition functional $Z_{EQG}$ in the ``little wormhole'' limit is real. Extension of the CM solutions with the inclusion of a bare cosmological constant to the case of a sphere $S^4$ can lead to the elimination of the destabilizing effects of the scalar modes of gravity against those of the matter. In particular, in the asymptotic region of a large 4-sphere, we recover the Coleman's $\exp \left (\exp \left ({1\over \lambda_{eff}}\right )\right )$ peak at the effective cosmological constant $\lambda_{eff}=0$, with no phase ambiguities in $Z_{EQG}$.Comment: 11 page

12j-symbols and four-dimensional quantum gravity

We propose a model which represents a four-dimensional version of Ponzano and Regge's three-dimensional euclidean quantum gravity. In particular we show that the exponential of the euclidean Einstein-Regge action for a $4d$-discretized block is given, in the semiclassical limit, by a gaussian integral of a suitable $12j$-symbol. Possible developments of this result are discussed.Comment: 12 pages, Late

Topological Yang-Mills cohomology in pure Yang-Mills Theory

Using the first order formalism (BFYM) of the Yang-Mills theory we show that it displays an embedded topological sector corresponding to the field content of the Topological Yang-Mills theory (TYM). This picture arises after a proper redefinition of the fields of BFYM and gives a clear representation of the non perturbative part of the theory in terms of the topological sector. In this setting the calculation of the $vev$ of a YM observable is translated into the calculation of a corresponding (non topological) quantity in TYM. We then compare the topological observables of TYM with a similar set of observables for BFYM and discuss the possibility of describing topological observables in YM theory.Comment: 12 pages, Latex, one reference added, to appear in Phys. Lett.