Natural and Gauge Natural Formalism for Classical Field Theorie: A Geometric Perspective Including Spinors and Gauge Theories

ISBN-13: 9789048164615 / Angielski / Miękka / 2010 / 365 str.

L. Fatibene; M. Francaviglia

Opis

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.

Spis treści

I The Geometric Setting; Introduction.- 1. Fiber Bundles.- 2. Jet Bundles.- 3. Principal Bundles and Connections.- 4. Natural Bundles.- 5. Gauge Natural Bundles.- II The Variational Structure of Field Theories; Introduction.- 6. The Lagrangian Formalism.- 7. Natural Theories.- 8. Gauge Natural Theories.- III Spinor Fields; Introduction.- 9. Spin Structures and Spin Frames.- 10. Spinor Theories.- Final Word.- References.- Analitic Index.