Beyond the TDHF: A collision term from a random-matrix model: P. Grangé, Centre de Recherches Nucléaires, Strasbourg, France; H. A. Weidenmüller, Max-Planck-Institut für Kernphysik, Heidelberg, Federal Republic of Germany; and G. Wolschin, Institut für theoretische Physik, Universität Heidelberg, Heidelberg, Federal Republic of Germany
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 78 KB
- Volume
- 135
- Category
- Article
- ISSN
- 0003-4916
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✦ Synopsis
We show within the Hamiltonian formalism the existence of classical relativistic mechanics of N scalar particles interacting at a distance which satisfies the requirements of Poincare invariance, separability, world-line invariance and Einstein causality. The line of approach which is adopted here uses the methods of the theory of systems with constraints applied to manifestly covariant systems of particles. The study is limited to the case of scalar interactions remaining weak in the whole phase space and vanishing at large space-like separation distances of the particles. Poincart invariance requires the inclusion of many-body, up to N-body, potentials. Separability requires the use of individual or two-body variables and the construction of the total interaction from basic two-body interactions. Position variables of the particles are constructed in terms of the canonical variables of the theory according to the world-line invariance condition and the subsidiary conditions of the non-relativistic limit and separability. Positivity constraints on the interaction masses squared of the particles ensure that the velocities of the latter remain always smaller than the velocity of light.