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Natural and Gauge Natural Formalism for Classical Field Theorie

A Geometric Perspective including Spinors and Gauge Theories

  • Book
  • © 2003

Overview

Authors:
  1. Lorenzo Fatibene

    1. Department of Mathematics, University of Torino, Italy

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  2. Mauro Francaviglia

    1. Department of Mathematics, University of Torino, Italy

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Table of contents (11 chapters)

  1. Front Matter

    Pages i-xxi
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  2. The Geometric Setting

    1. Front Matter

      Pages 1-6
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    2. Fiber Bundles

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 9-51

    3. Jet Bundles

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 53-78

    4. Principal Bundles and Connections

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 79-112

    5. Natural Bundles

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 113-124

    6. Gauge Natural Bundles

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 125-142

  3. The Varaiational Structure of Field Theories

    1. Front Matter

      Pages 143-149
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    2. The Lagrangian Formalism

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 151-217

    3. Natural Theories

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 219-268

    4. Gauge Natural Theories

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 269-291

  4. Spinor Fields

    1. Front Matter

      Pages 293-298
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    2. Spin Structures and Spin Frames

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 299-323

    3. Spinor Theories

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 325-347

    4. Final word

      • Lorenzo Fatibene, Mauro Francaviglia
      Pages 349-352

  5. Back Matter

    Pages 353-365
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Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, University of Torino, Italy

    Lorenzo Fatibene, Mauro Francaviglia

Bibliographic Information

  • Book Title: Natural and Gauge Natural Formalism for Classical Field Theorie

  • Book Subtitle: A Geometric Perspective including Spinors and Gauge Theories

  • Authors: Lorenzo Fatibene, Mauro Francaviglia

  • DOI: https://doi.org/10.1007/978-94-017-2384-8

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2003

  • Hardcover ISBN: 978-1-4020-1703-2Published: 30 November 2003

  • Softcover ISBN: 978-90-481-6461-5Published: 01 December 2010

  • eBook ISBN: 978-94-017-2384-8Published: 29 June 2013

  • Edition Number: 1

  • Number of Pages: XXI, 365

  • Topics: Theoretical, Mathematical and Computational Physics, Applications of Mathematics, Differential Geometry, Classical Mechanics

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