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Noether's Theorems

Applications in Mechanics and Field Theory

  • Book
  • © 2016

Overview

Authors:
  1. Gennadi Sardanashvily

    1. Moscow State University, Moscow, Russia

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  • Noether's theorems are presented in the most general and universal form
  • The calculus of variations and Lagrangian theory are formulated in a very general setting
  • Relevant examples from mechanics and field theory help the reader to understand the general theory of Noether's theorems and their applications in physics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Atlantis Studies in Variational Geometry (ASVG, volume 3)

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Table of contents (12 chapters)

  1. Front Matter

    Pages i-xvii
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  2. Calculus of Variations on Fibre Bundles

    • Gennadi Sardanashvily
    Pages 1-15

  3. Noether’s First Theorem

    • Gennadi Sardanashvily
    Pages 17-25

  4. Lagrangian and Hamiltonian Field Theories

    • Gennadi Sardanashvily
    Pages 27-57

  5. Lagrangian and Hamiltonian Nonrelativistic Mechanics

    • Gennadi Sardanashvily
    Pages 59-92

  6. Global Kepler Problem

    • Gennadi Sardanashvily
    Pages 93-101

  7. Calculus of Variations on Graded Bundles

    • Gennadi Sardanashvily
    Pages 103-133

  8. Noether’s Second Theorems

    • Gennadi Sardanashvily
    Pages 135-161

  9. Yang–Mills Gauge Theory on Principal Bundles

    • Gennadi Sardanashvily
    Pages 163-181

  10. SUSY Gauge Theory on Principal Graded Bundles

    • Gennadi Sardanashvily
    Pages 183-188

  11. Gauge Gravitation Theory on Natural Bundles

    • Gennadi Sardanashvily
    Pages 189-200

  12. Chern–Simons Topological Field Theory

    • Gennadi Sardanashvily
    Pages 201-206

  13. Topological BF Theory

    • Gennadi Sardanashvily
    Pages 207-210

  14. Back Matter

    Pages 211-297
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Keywords

About this book

The book provides a detailed exposition of the calculus of variations on fibre bundles and graded manifolds. It presents applications in such area's as non-relativistic mechanics, gauge theory, gravitation theory and topological field theory with  emphasis on energy and energy-momentum conservation laws. Within this general context the first and second Noether theorems are treated in the very general setting of reducible degenerate graded Lagrangian theory.

Reviews

“This book contains a systematic and detailed approach to Lagrangian systems through the variational bicomplex providing a very general geometric and algebraic view of the variational calculus. … The book is very well written in a clear and direct style containing very helpful cross references. In addition the book under review includes 4 appendices which make the presentation self contained.” (Miguel Paternain, zbMATH 1357.58002, 2017)

Authors and Affiliations

  • Moscow State University, Moscow, Russia

    Gennadi Sardanashvily

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