Angular Momentum and Energy of a Multiparticle System

Bruce Cameron Reed

Mark S. Swanson

Chapter 7 introduces the concepts of symmetry operations and then focuses on rotation. The general properties of angular momentum and spin are derived. Multiparticle systems are introduced and angular momentum addition is analyzed.

Peter Woit

H. E. Moses, S. C. Wang

Jamal Sakhr

For the periodic orbit quantization of a system of particles confined in a two-dimensional disk billiard, the proliferation of multiparticle periodic orbits with length precludes standard length truncation of the trace formula and alternative truncation schemes are necessary. An amplitude ordering of the single-particle periodic orbits reveals a quantum-classical correspondence for the angular momentum of a particle in the disk which is useful for the quantization of all the low energy states of the multiparticle problem. We explicitly show that a simple amplitude truncation of the trace formula better approximates the semiclassical density of states and in particular resolves closely spaced levels that are otherwise unresolved using the standard approach.

Roger F. Dashen, Shang-keng Ma

We have shown earlier how the virial coefficients can be expressed in terms of traces taken over products of multiparticle (on-energy-shell) scattering matrices. The traces are to be taken in the angular-momentum representation instead of the momentum representation to avoid the infinite forward N-particle scattering amplitude for N > 2 caused by certain singular diagrams. Here, we analyze and sum the contribution of the singular diagrams to the third virial coefficient. It is also shown that one can get the same result if off-shell amplitudes in the momentum representation are utilized.