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In this paper we study the behavior of the Casimir energy of a "multi-cavity" across the transition from the metallic to the superconducting phase of the constituting plates. Our analysis is carried out in the framework of the ARCHIMEDES experiment, aiming at measuring the interaction of the electromagnetic vacuum energy with a gravitational field. For this purpose it is foreseen to modulate the Casimir energy of a layered structure composing a multi-cavity coupled system by inducing a transition from the metallic to the superconducting phase. This implies a thorough study of the behavior of the cavity, where normal metallic layers are alternated with superconducting layers, across the transition. Our study finds that, because of the coupling between the cavities, mainly mediated by the transverse magnetic modes of the radiation field, the variation of energy across the transition can be very large., Comment: 17 pages, 3 figures. Abstract and title slightly modified. Figures and comments added

The quantum-to-classical transition is considered from the point of view of contractions of associative algebras. Various methods and ideas to deal with contractions of associative algebras are discussed that account for a large family of examples. As an instance of them, the commutative algebra of functions in phase space, corresponding to classical physical observables, is obtained as a contraction of the Moyal star-product which characterizes the quantum case. Contractions of associative algebras associated to Lie algebras are discussed, in particular the Weyl-Heisenberg and $SU(2)$ groups are considered., Comment: 21 pages, 1 figure

The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit, photon-number (Fock) states and symplectic tomography quantizers and dequantizers will be constructed. Conditions for identifying the convolution product of groupoid functions and the star--product arising from a quantization--dequantization scheme will be given. A tomographic approach to construct quasi--distributions out of suitable immersions of groupoids into Hilbert spaces will be formulated and, finally, intertwining kernels for such generalized symplectic tomograms will be evaluated explicitly.

The quantizer-dequantizer method allows to construct associative products on any measure space. Here we consider an inverse problem: given an associative product is it possible to realize it within the quantizer-dequantizer framework? The answer is positive in finite dimensions and we give a few examples in infinite dimensions., Comment: 13 pages. To appear on Physica Scripta

This work is devoted to study the deformation of spacetime metrics as generalized conformal transformations. Some applications are also considered, in particular the equations of motion in deformed spacetime are studied., Comment: 5 pages. To appear in the proceedings of 3rd Stueckelberg Workshop on Relativistic Field Theories, Pescara, Italy, 8-18 Jul 2008

Classical and quantum perturbations can be described in terms of marginal distribution functions in the framework of tomographic cosmology. In particular, the so called Radon transformation and the mode-parametric quantum oscillator description can give rise to links between quantum and classical regimes. The approach results a natural scheme to discuss the transition from the quantum to the classical perturbations and then it could be a workable scheme to connect primordial fluctuations with the today observed large scale structure., Comment: 12 pages

f(R)-gravity with geometric torsion (not related to any spin fluid) is considered in a cosmological context. We derive the field equations in vacuum and in presence of perfect-fluid matter and discuss the related cosmological models. Torsion vanishes in vacuum for almost all arbitrary functions f(R) leading to standard General Relativity. Only for f(R)=R^{2}, torsion gives contribution in the vacuum leading to an accelerated behavior . When material sources are considered, we find that the torsion tensor is different from zero even with spinless material sources. This tensor is related to the logarithmic derivative of f'(R), which can be expressed also as a nonlinear function of the trace of the matter energy-momentum tensor. We show that the resulting equations for the metric can always be arranged to yield effective Einstein equations. When the homogeneous and isotropic cosmological models are considered, terms originated by torsion can lead to accelerated expansion. This means that, in f(R) gravity, torsion can be a geometric source for acceleration., Comment: 13 pages

We discuss the f(R)-theories of gravity with torsion in the framework of jet-bundles. Such an approach is particularly useful since the components of the torsion and curvature tensors can be chosen as fiber jet-coordinates on the bundles and then the symmetries and the conservation laws of the theory can be easily achieved. Field equations of f(R)-gravity are studied in empty space and in presence of various forms of matter as Dirac fields, Yang--Mills fields and spin perfect fluid. Such fields enlarge the jet-bundles framework and characterize the dynamics. Finally we give some cosmological applications and discuss the relations between f(R)-gravity and scalar-tensor theories., Comment: 17 pages

A definition of space-time metric deformations on an $n$-dimensional manifold is given. We show that such deformations can be regarded as extended conformal transformations. In particular, their features can be related to the perturbation theory giving a natural picture by which gravitational waves are described by small deformations of the metric. As further result, deformations can be related to approximate Killing vectors (approximate symmetries) by which it is possible to parameterize the deformed region of a given manifold. The perspectives and some possible physical applications of such an approach are discussed., Comment: 9 pages

The role of torsion in f(R) gravity is considered in the framework of metric-affine formalism. We discuss the field equations in empty space and in presence of perfect fluid matter taking into account the analogy with the Palatini formalism. As a result, the extra curvature and torsion degrees of freedom can be dealt as an effective scalar field of fully geometric origin. From a cosmological point of view, such a geometric description could account for the whole Dark Side of the Universe., Comment: 12 pages

The probability representation, in which cosmological quantum states are described by a standard positive probability distribution, is constructed for minisuperspace models selected by Noether symmetries. In such a case, the tomographic probability distribution provides the classical evolution for the models and can be considered an approach to select "observable" universes. Some specific examples, derived from Extended Theories of Gravity, are worked out. We discuss also how to connect tomograms, symmetries and cosmological parameters., Comment: 15 pages

In this paper we review the properties of the black hole entropy in the light of a general conformal field theory treatment. We find that the properties of horizons of the BTZ black holes in ADS_{3}, can be described in terms of an effective unitary CFT_{2} with central charge c=1 realized in terms of the Fubini-Veneziano vertex operators. It is found a relationship between the topological properties of the black hole solution and the infinite algebra extension of the conformal group in 2D, SU(2,2), i.e. the Virasoro Algebra, and its subgroup SL(2,Z) which generates the modular symmetry. Such a symmetry induces a duality for the black hole solution with angular momentum J\neq 0. On the light of such a global symmetry we reanalyze the Cardy formula for CFT_{2} and its possible generalization to D>2 proposed by E. Verlinde., Comment: 21 pages

The probability representation for quantum states of the universe in which the states are described by a fair probability distribution instead of wave function (or density matrix) is developed to consider cosmological dynamics. The evolution of the universe state is described by standard positive transition probability (tomographic transition probability) instead of the complex transition probability amplitude (Feynman path integral) of the standard approach. The latter one is expressed in terms of the tomographic transition probability. Examples of minisuperspaces in the framework of the suggested approach are presented. Possibility of observational applications of the universe tomographs are discussed., Comment: 16 pages

The notion of standard positive probability distribution function (tomogram) which describes the quantum state of universe alternatively to wave function or to density matrix is introduced. Connection of the tomographic probability distribution with the Wigner function of the universe and with the star-product (deformation) quantization procedure is established. Using the Radon transform the Wheeler-De Witt generic equation for the probability function is written in tomographic form. Some examples of the Wheeler-DeWitt equation in the minisuperspace are elaborated explicitly for a homogeneous isotropic cosmological models. Some interpretational aspects of the probability description of the quantum state are discussed., Comment: 22 pages LaTeX, some minor corrections, new references added, submitted to General Relativity and Gravitation

A set of brackets for classical dissipative systems, subject to external random forces, are derived. The method is inspired to the old procedure found by Peierls, for deriving the canonical brackets of conservative systems, starting from an action principle. It is found that an adaptation of Peierls' method is applicable also to dissipative systems, when the friction term can be described by a linear functional of the coordinates, as is the case in the classical Langevin equation, with an arbitrary memory function. The general expression for the brackets satisfied by the coordinates, as well as by the external random forces, at different times, is determined, and it turns out that they all satisfy the Jacobi identity. Upon quantization, these classical brackets are found to coincide with the commutation rules for the quantum Langevin equation, that have been obtained in the past, by appealing to microscopic conservative quantum models for the friction mechanism., Comment: 4 pages

The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to the torsion fields and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth order curvature or torsion theories so that we obtain an alternative scheme to the standard quintessence scalar field, minimally coupled to gravity, usually adopted. We discuss also conformal transformations in order to see the links of quintessence between the Jordan and Einstein frames. Furthermore, we take into account a torsion fluid whose effects become relevant at large scale. Specifically, we investigate a model where a totally antisymmetric torsion field is taken into account discussing the conditions to obtain quintessence. We obtain exact solutions also in this case where dust dominated Friedmann behavior is recovered as soon as torsion effects are not relevant., Comment: 12 pages, proceedings of COSMO-01

Torsion appears in literature in quite different forms. Generally, spin is considered to be the source of torsion, but there are several other possibilities in which torsion emerges in different contexts. In some cases a phenomenological counterpart is absent, in some other cases torsion arises from sources without spin as a gradient of a scalar field. Accordingly, we propose two classification schemes. The first one is based on the possibility to construct torsion tensors from the product of a covariant bivector and a vector and their respective space-time properties. The second one is obtained by starting from the decomposition of torsion into three irreducible pieces. Their space-time properties again lead to a complete classification. The classifications found are given in a U_4, a four dimensional space-time where the torsion tensors have some peculiar properties. The irreducible decomposition is useful since most of the phenomenological work done for torsion concerns four dimensional cosmological models. In the second part of the paper two applications of these classification schemes are given. The modifications of energy-momentum tensors are considered that arise due to different sources of torsion. Furthermore, we analyze the contributions of torsion to shear, vorticity, expansion and acceleration. Finally the generalized Raychaudhuri equation is discussed., Comment: LATEX file, 18 pages, accepted for Publication in Annalen der Physik

We show that in theories of gravitation with torsion the helicity of fermion particles is not conserved and we calculate the probability of spin flip, which is related to the anti-symmetric part of affine connection. Some cosmological consequences are discussed., Comment: 6 pages, to appear in Europhysics Letters

We extend a previous analysis concerning cosmological fluids with generalized equations of state in order to study inflationary scenarios. In the framework of the slow-roll approximation we find the expressions for the perturbation parameters $\epsilon$, $\eta$ and the density perturbation spectra in terms of the adiabatic index $\ga$ as a function of the universe scale factor. This connection allows to find straightforwardly $\ga$ corresponding, for example, to the simplest {\it chaotic} model and to the Harrison-Zeldovich potential and shows its capability to be applied to more complicate situations. Finally, we use this description to develop a new approach to the early universe dynamics, based on a $1/N$ expansion, where $N$ is the e-fold number. To this aim, we introduce a set of suitable dimensionless variables and show that at the zero-th order in $1/N$, an improved slow-roll approximation is obtained., Comment: 15 pages, plain Latex, to appear in Mod. Phys. Lett. A

The Lagrangian formulation of classical field theories and in particular general relativity leads to a coordinate-free, fully covariant analysis of these constrained systems. This paper applies multisymplectic techniques to obtain the analysis of Palatini and self-dual gravity theories as constrained systems, which have been studied so far in the Hamiltonian formalism. The constraint equations are derived while paying attention to boundary terms, and the Hamiltonian constraint turns out to be linear in the multimomenta. The equivalence with Ashtekar's formalism is also established. The whole constraint analysis, however, remains covariant in that the multimomentum map is evaluated on {\it any} spacelike hypersurface. This study is motivated by the non-perturbative quantization program of general relativity., Comment: 22 pages, plain Tex, no figures, accepted for publication in Nuovo Cimento B