On the spectral analysis of many-body systems
Abstract
We describe the essential spectrum and prove the Mourre estimate for quantum particle systems interacting through k-body forces and creation-annihilation processes which do not preserve the number of particles. For this we compute the ``Hamiltonian algebra'' of the system, i.e. the C*-algebra C generated by the Hamiltonians we want to study, and show that, as in the N-body case, it is graded by a semilattice. Hilbert C*-modules graded by semilattices are involved in the construction of C. For example, if we start with an N-body system whose Hamiltonian algebra is B and then we add field type couplings between subsystems, then the many-body Hamiltonian algebra C is the imprimitivity algebra of a graded Hilbert B-module.
Keywords
Cite
@article{arxiv.0911.5126,
title = {On the spectral analysis of many-body systems},
author = {Mondher Damak and Vladimir Georgescu},
journal= {arXiv preprint arXiv:0911.5126},
year = {2009}
}
Comments
This is a strongly modified version of arXiv:0806.0827v1 so we preferred to change the title