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Lectures on Hyperhamiltonian Dynamics and Physical Applications

  • Giuseppe Gaeta
  • Miguel A. Rodríguez

Part of the Mathematical Physics Studies book series (MPST)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 1-16
  3. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 17-36
  4. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 37-62
  5. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 63-82
  6. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 83-105
  7. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 107-138
  8. Giuseppe Gaeta, Miguel A. Rodríguez
    Pages 139-158
  9. Back Matter
    Pages 159-182

About this book

Introduction

This book provides the mathematical foundations of the theory of hyperhamiltonian dynamics, together with a discussion of physical applications. In addition, some open problems are discussed. Hyperhamiltonian mechanics represents a generalization of Hamiltonian mechanics, in which the role of the symplectic structure is taken by a hyperkähler one (thus there are three Kähler/symplectic forms satisfying quaternionic relations). This has proved to be of use in the description of physical systems with spin, including those which do not admit a Hamiltonian formulation. The book is the first monograph on the subject, which has previously been treated only in research papers.

Keywords

Hyperhamiltonian dynamics Quaternionic structures Spin systems in quantum mechanics Hyperkähler manifolds Lie groups and holonomy

Authors and affiliations

  • Giuseppe Gaeta
    • 1
  • Miguel A. Rodríguez
    • 2
  1. 1.Dipartimento di MatematicaUniversità degli Studi di Milano Dipartimento di MatematicaMilanoItaly
  2. 2.Departamento de Física TeóricaUniversidad Complutense de Madrid Departamento de Física TeóricaMadridSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-54358-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-54357-4
  • Online ISBN 978-3-319-54358-1
  • Series Print ISSN 0921-3767
  • Series Online ISSN 2352-3905
  • Buy this book on publisher's site