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Papers by Lorenzo Fatibene

World Conference on …, Jun 25, 2007

Art and Mathematics evolved in parallel, alongwith changes in our ways of conceiving and represen... more Art and Mathematics evolved in parallel, alongwith changes in our ways of conceiving and representing" reality": Classical Art (rigidity of Euclidean Geometry); Perspective and Projective Geometry (points at infinity as ordinary); non-Euclidean Geometry;" Synthetic Geometry" and deconstruction of rigid forms. Web Technologies and Multimediality offer new ways to introduce Mathematics starting from artworks. We discuss an innovative" teaching/visualization project" based on the Web, in 4 major parts: 1) a ...

We show how the ad hoc prescriptions appeared in 2001 by Ortin for the Lie derivative of Lorentz ... more We show how the ad hoc prescriptions appeared in 2001 by Ortin for the Lie derivative of Lorentz tensors are a direct consequence of the Kosmann lift defined earlier in 1996 in a much more general setting encompassing older results of Y. Kosmann in 1971. Comment: Typos corrected, references added, some application added. 11 pages

International Journal of Geometric Methods in Modern Physics

We shall present and analyze two examples of extended theories of gravitation in Palatini formali... more We shall present and analyze two examples of extended theories of gravitation in Palatini formalism with matter that couples to the connection. This will show that the class of Further Extended Theories of Gravitation introduced in [1] does not trivially reduce to f(R) models. It will also produce an example of theory that on-shell endows space–time with a non-trivial Weyl geometry where the connection is not induced by the metric structure (though it is compatible with it in the sense of Ehlers–Pirani–Schild; see [2]).

It is shown that when in a higher order variational principle one fixes fields at the boundary le... more It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particularl by the need of clarifying the issue for the purpose of applications to relativistic gravitational theories, where a bit of confusion still exists. On the contrary, as it is well known for variational principles of order k, if one fixes variables together with their derivatives (up to order k-1) on the boundary then boundary terms leave solution space invariant.

General Relativity and Gravitation - GEN RELATIV GRAVIT, 2000

A two-spinor formalism for the Einstein Lagrangian is developed. The gravitational field is regar... more A two-spinor formalism for the Einstein Lagrangian is developed. The gravitational field is regarded as a composite object derived from soldering forms. Our formalism is geometrically and globally well-defined and may be used in virtually any 4m-dimensional manifold with arbitrary signature as well as without any stringent topological requirement on space-time, such as parallelizability. Interactions and feedbacks between gravity and spinor fields are considered. As is well known, the Hilbert–Einstein Lagrangian is second order also when expressed in terms of soldering forms. A covariant splitting is then analysed leading to a first-order Lagrangian which is recognized to play a fundamental role in the theory of conserved quantities. The splitting and thence the first-order Lagrangian depend on a reference spin connection which is physically interpreted as setting the zero level for conserved quantities. A complete and detailed treatment of conserved quantities is then presented.

Symmetry, Integrability and Geometry: Methods and Applications, 2011

It is shown that the second order symmetry operators for the Dirac equation on a general two-dime... more It is shown that the second order symmetry operators for the Dirac equation on a general two-dimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.

International Journal of Geometric Methods in Modern Physics, 2014

International Journal of Geometric Methods in Modern Physics, 2006

We investigate the covariant formulation of Chern-Simons theories in a general odd dimension whic... more We investigate the covariant formulation of Chern-Simons theories in a general odd dimension which can be obtained by introducing a vacuum connection field as a reference. Field equations, Nöther currents and superpotentials are computed so that results are easily compared with the wellknown results in dimension 3. Finally we use this covariant formulation of Chern-Simons theories to investigate their relation with topological BF theories.

International Journal of Geometric Methods in Modern Physics, 2008

ABSTRACT In the framework of augmented variational principles we recover here the conserved quant... more ABSTRACT In the framework of augmented variational principles we recover here the conserved quantities proposed by Gibbons at al. for Kerr-AdS solutions.

International Journal of Geometric Methods in Modern Physics, 2012

We discuss in a critical way the physical foundations of geometric structure of relativistic theo... more We discuss in a critical way the physical foundations of geometric structure of relativistic theories of gravity by the so-called Ehlers-Pirani-Schild formalism. This approach provides a natural interpretation of the observables showing how relate them to General Relativity and to a large class of Extended Theories of Gravity. In particular we show that, in such a formalism, geodesic and causal structures of space-time can be safely disentangled allowing a correct analysis in view of observations and experiment. As specific case, we take into account the case of f (R) gravity.

Entropy, 2007

We shall review different approaches to the entropy of self-gravitating systems in General Relati... more We shall review different approaches to the entropy of self-gravitating systems in General Relativity. Then we shall discuss in detail the macroscopic approach based onà la Clausius point of view. Recent developments will be reviewed discussing the aims as well as the assumptions which the framework is based on.

ABSTRACT We shall show that although Palatini f(R)-theories are equivalent to Brans-Dicke theorie... more ABSTRACT We shall show that although Palatini f(R)-theories are equivalent to Brans-Dicke theories, still the first pass the Mercury precession of perihelia test, while the second do not. We argue that the two models are not physically equivalent due to a different assumptions about free fall. We shall also go through perihelia test without fixing a conformal gauge (clocks or rulers) in order to highlight what can be measured in a conformal invariant way and what cannot. We shall argue that the conformal gauge is broken by choosing a definition of clock, rulers or, equivalently, of masses.

It is shown that the second order symmetry operators for the Dirac equation on a general twodimen... more It is shown that the second order symmetry operators for the Dirac equation on a general twodimensional spin manifold may be expressed in terms of Killing vectors and valence two Killing tensors. The role of these operators in the theory of separation of variables for the Dirac equation is studied.