Classical Grand Angular Momentum in N-Body Problems
Zhongqi Liang, Jes\'us P\'erez-R\'ios
TL;DR
This paper extends the concept of grand angular momentum from quantum to classical N-body problems, providing new decompositions and a general scattering angle formula using tree representations of coordinates.
Contribution
It introduces a classical analysis of grand angular momentum in N-body problems and derives a general scattering angle expression using tree representations.
Findings
Decomposition of grand angular momentum into one-body angular momenta.
General expression for scattering angle in N-body problems.
Extension of two-body results to N-body classical systems.
Abstract
The concept of grand angular momentum is widely used in the study of N-body problems quantum mechanically. Here, we applied it to a classical analysis of N-body problems. Utilizing the tree representation for Jacobi and hyperspherical coordinates, we found a decomposition of its magnitude into magnitudes of one-body angular momenta in three dimensions. We generalized some results from the two-body case and derived a general expression for the scattering angle in N-body problems.
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