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Hamiltonian Field Theory in the Radiating Regime

  • Book
  • © 2002

Overview

Authors:
  1. Piotr T. Chruściel

    1. Département de Mathématiques, Faculté des Sciences, Université de Tours, Tours, France

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  2. Jacek Jezierski

    1. Department of Mathematical Methods in Physics, University of Warsaw, Warsaw, Poland

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  3. Jerzy Kijowski

    1. Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

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  • Original research dealing with the difficult problem of a Hamiltonian formalism for classical field theories
  • No recent book on this issue exists
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 70)

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Table of contents (6 chapters)

  1. Front Matter

    Pages I-VI
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  2. Introduction

    Pages 1-5

  3. Preliminaries

    Pages 7-21

  4. Hamiltonian flows for geometric field theories

    Pages 23-39

  5. Radiating scalar fields

    Pages 41-63

  6. The energy of the gravitational field

    Pages 65-104

  7. Hamiltonians associated with the BMS group

    Pages 105-137

  8. Back Matter

    Pages 139-172
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About this book

The purpose of this monograph is to show that, in the radiation regime, there exists a Hamiltonian description of the dynamics of a massless scalar field, as well as of the dynamics of the gravitational field. The authors construct such a framework extending the previous work of Kijowski and Tulczyjew. They start by reviewing some elementary facts concerning Hamiltonian dynamical systems and then describe the geometric Hamiltonian framework, adequate for both the usual asymptotically-flat-at-spatial-infinity regime and for the radiation regime. The text then gives a detailed description of the application of the new formalism to the case of the massless scalar field. Finally, the formalism is applied to the case of Einstein gravity. The Hamiltonian role of the Trautman--Bondi mass is exhibited. A Hamiltonian definition of angular momentum at null infinity is derived and analysed.

Reviews

"The text is addressed to physicists and is not written in theorem-proof style, nor are the function spaces introduced equipped with explicit topologies and differentiable structures. However, all concepts are very carefully defined and necessary deviations from a rigorous treatment are clearly identified." (Mathematical Reviews 2003f)

"This monograph gives a comprehensive overview about Hamiltonian field theory with main application to the Einstein field equation. [...] Carefully prepared appendices and bibliography close this very readable book." (Zentralblatt MATH, 1002/02, 2003)

Authors and Affiliations

  • Département de Mathématiques, Faculté des Sciences, Université de Tours, Tours, France

    Piotr T. Chruściel

  • Department of Mathematical Methods in Physics, University of Warsaw, Warsaw, Poland

    Jacek Jezierski

  • Center for Theoretical Physics, Polish Academy of Sciences, Warsaw, Poland

    Jerzy Kijowski

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