Ultrarelativistic N-boson systems

TL;DR

This paper derives analytical energy bounds for ultrarelativistic N-boson systems with attractive pair potentials, proving a lower bound using a translation-invariant model Hamiltonian and providing accurate energy estimates for linear potentials.

Contribution

It establishes a general proof that a translation-invariant Hamiltonian provides a lower energy bound for all N-boson systems, extending previous results beyond N=4.

Findings

Proved the lower bound for all N ≥ 2.

Achieved energy estimates with less than 0.55% error for linear potential.

Extended the validity of the lower bound conjecture to all N.

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.