Hamiltonian Field Theory in the Radiating Regime: Lecture Notes in Physics Monographs, cartea 70

Preliminaries.- Hamiltonian flows for geometric field theories.- Radiating scalar fields.- The energy of the gravitational field.- Hamiltonians associated with the BMS group.

"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)

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.

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