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 book 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 Nother currents and conserved integrals. This is the first comprehensive, organic and self-contained introduction to this new fascinating area and it contains a number of fully worked examples which show the power of the framework. This book is of interest to researchers and graduate students in the fields of theoretical physics, mathematical physics as well as differential geometry.