Chrusciel P.T., Jezierski J., Kijowski J. Hamiltonian Field Theory in the Radiating Regime

Springer-Verlag Berlin Heidelberg, 2002 — 174p. — (Lecture Notes in Physics Monographs 70) — ISBN: 978-3-540-45604-9 (eBook), 978-3-642-07681-7 (Softcover), 978-3-540-42884-8 (Hardcover).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.Preliminaries
Hamiltonian flows for geometric field theories
Radiating scalar fields
The energy of the gravitational field
Hamiltonians associated with the BMS group