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We give a general expression for the static potential energy of the gravitational interaction of two massive particles, in terms of an invariant vacuum expectation value of the quantized gravitational field. This formula holds for functional integral formulations of euclidean quantum gravity, regularized to avoid conformal instability. It could be regarded… (More)

The positive energy theorem precludes the possibility of Minkowski flat space decaying by any mechanism. In certain circumstances, however, large quantum fluctuations of the gravitational field could arise—not only at the Planck scale, but also at larger scales. This is because there exists a set of localised weak field configurations which satisfy the… (More)

A Wilson loop is defined, in 4-D pure Einstein gravity, as the trace of the holonomy of the Christoffel connection or of the spin connection, and its invariance under the symmetry transformations of the action is showed (diffeomorphisms and local Lorentz transformations). We then compute the loop perturbatively, both on a flat background and in the presence… (More)

We discuss a family of models expressed by nonlinear differential equation systems describing closed market societies in the presence of taxation and redistribution. We focus in particular on three example models obtained in correspondence to different parameter choices. We analyse the influence of the various choices on the long time shape of the income… (More)

Under special conditions (Meissner-effect levitation in a high frequency magnetic field and rapid rotation) a disk of high-Tc superconducting material has recently been found to produce a weak shielding of the gravitational field. We show that this phenomenon has no explanation in the standard gravity theories, except possibly in the non-perturbative… (More)

- Maria Letizia Bertotti, Giovanni Modanese
- Complexity
- 2016

We formulate a flexible micro-to-macro kinetic model which is able to explain the emergence of income profiles out of a whole of individual economic interactions. The model is expressed by a system of several nonlinear differential equations which involve parameters defined by probabilities. Society is described as an ensemble of individuals divided into… (More)

- Maria Letizia Bertotti, Giovanni Modanese
- Applied Mathematics and Computation
- 2014

We investigate the effect of tax evasion on the income distribution and the inequality index of a society through a kinetic model described by a set of nonlinear ordinary differential equations. The model allows to compute the global outcome of binary and multiple microscopic interactions between individuals. When evasion occurs, both individuals involved… (More)

We study a novel set of gravitational field configurations, called “dipolar zero modes”, which give an exactly null contribution to the Einstein action and are thus candidates to become large fluctuations in the quantized theory. They are generated by static unphysical sources satisfying (up to terms of order G) the simple condition ∫ dxT00(x) = 0. We give… (More)

It was recently suggested that the gravitational action could contain a scale-dependent cosmological term, depending on the length or momentum scale characteristic of the processes under consideration. In this work we explore a simple possible consequence of this assumption. We compute the field generated in empty space by a static spherical source (the… (More)

In 4D non-perturbative Regge calculus a positive value of the effective cosmological constant characterizes the collapsed phase of the system. If a local term of the form S′ =