Metric fluctuations and the Weak Equivalence Principle

We describe space--time fluctuations by means of small fluctuations of the metric on a given background metric. From a minimally coupled Klein--Gordon equation we obtain within a weak-field approximation up to second order and an averaging procedure over a finite space--time scale given by the quantum particle in the non--relativistic limit a modified Schr\"odinger equation. The dominant modification consists in an anomalous inertial mass tensor which depends on the type of particle and on the fluctuation scenario. The scenario considered in this paper is a most simple picture of spacetime fluctuations and gives an existence proof for an apparent violation of the weak equivalence principle and, in general, for a violation of Lorentz invariance.Comment: 10 pages, to appear in Class. Quantum Grav. (2008

Consistent couplings between spin-2 and spin-3 massless fields

We solve the problem of constructing consistent first-order cross-interactions between spin-2 and spin-3 massless fields in flat spacetime of arbitrary dimension n > 3 and in such a way that the deformed gauge algebra is non-Abelian. No assumptions are made on the number of derivatives involved in the Lagrangian, except that it should be finite. Together with locality, we also impose manifest Poincare invariance, parity invariance and analyticity of the deformations in the coupling constants.Comment: LaTeX file. 29 pages, no figures. Minor corrections. Accepted for publication in JHE

Spin three gauge theory revisited

We study the problem of consistent interactions for spin-3 gauge fields in flat spacetime of arbitrary dimension n>3. Under the sole assumptions of Poincar\'e and parity invariance, local and perturbative deformation of the free theory, we determine all nontrivial consistent deformations of the abelian gauge algebra and classify the corresponding deformations of the quadratic action, at first order in the deformation parameter. We prove that all such vertices are cubic, contain a total of either three or five derivatives and are uniquely characterized by a rank-three constant tensor (an internal algebra structure constant). The covariant cubic vertex containing three derivatives is the vertex discovered by Berends, Burgers and van Dam, which however leads to inconsistencies at second order in the deformation parameter. In dimensions n>4 and for a completely antisymmetric structure constant tensor, another covariant cubic vertex exists, which contains five derivatives and passes the consistency test where the previous vertex failed.Comment: LaTeX, 37 pages. References and comments added. Published versio