Ultrarelativistic N-boson systems
Mathematical Physics
2011-11-10 v1 math.MP
Abstract
General analytic energy bounds are derived for N-boson systems governed by ultrarelativistic Hamiltonians of the form H = sum_{i=1}^N||p_i|| + sum_{1=i<j}^N V(r_{ij}), where V(r) is a static attractive pair potential. It is proved that a translation-invariant model Hamiltonian H_c provides a lower bound to H for all N \ge 2. This result was conjectured in an earlier paper but proved only for N = 2,3,4. As an example, the energy in the case of the linear potential V(r) = r is determined with error less than 0.55% for all N \ge 2.
Cite
@article{arxiv.0706.0710,
title = {Ultrarelativistic N-boson systems},
author = {Richard L. Hall and Wolfgang Lucha},
journal= {arXiv preprint arXiv:0706.0710},
year = {2011}
}