M. Francaviglia – författare

The mathematical theory of gauge natural bundles has recently been developed to provide a natural mathematical framework for gauge covariant fields (principal connections and associated objects). For this reason the language and the techniques of gauge natural bundles provide a privileged unifying scheme to treat the dynamics of all classical field theories. In this volume the authors develop and work out applications to gravity and gauge theories and their interactions with generic matter fields, including spinors in full detail. Spinor fields in particular appear to be the prototypes of truly gauge-natural objects, which are not purely gauge nor purely natural, so that they are a paradigmatic example of the intriguing relations between gauge natural geometry and physical phenomenology. In particular, the gauge natural framework for spinors is developed in this book in full detail, and it is shown to be fundamentally related to the interaction between fermions and dynamical tetrad gravity.The gauge natural framework also provides an extended area to deal with conservation laws and it encompasses all apparently unrelated covariant prescriptions commonly used in relativistic theories to generate other currents and conserved integrals. This book should be of interest to researchers and graduate students in the fields of theoretical physics, mathematical physics as well as differential geometry.

This volume contains the proceedings of a summer school presented by the Centro Internazionale Matematico Estivo, held at Montecatini Terme, Italy, in July 1988. This summer programme was devoted to methods of global differential geometry and algebraic geometry in field theory, with the main emphasis on istantons, vortices and other similar structures in gauge theories; Riemann surfaces and conformal field theories; geometry of supermanifolds and applications to physics. The papers are mainly surveys and tutorials.

The book is the result of the Italian conference on General Relativity, held in Italy in September 1998. One of the main features of this conference has been to bring together mathematicians and physicists, experts in different fields: General Relativity, Variational and Topological methods, Differential Geometry, Astrophysics. Classical and Quantum aspects of General Relativity have been debated and various new results have been presented. Perspectives on the search of Gravitational waves have been illustrated. These methods permit to study the geodesical connectedness of space-times and to relate to topological properties to the multiplicity of the geodesics joining two given events. Critical point Morse theory has been used to study light rays on Lorentzian manifolds and to interpret the gravitational lensing effect.

A survey of the most recent developments in general relativity and in the theory of the unification of Fundamental Interactions is presented in this book. The theoretical results, the cosmological and astrophysical aspects, the experimental and observational programs are shown in 26 general talks by renowned scientists active in this field.