Gravitating semirelativistic N-boson systems

TL;DR

This paper derives analytic energy bounds for N-boson systems with semirelativistic Hamiltonians, providing tighter bounds for gravitational interactions and confirming consistency with nonrelativistic results.

Contribution

It introduces new analytic bounds for semirelativistic N-boson systems, improving upon previous bounds especially in gravitational cases.

Findings

Tighter energy bounds for gravity v=c/N

Bounds match known nonrelativistic results

Applicable to semirelativistic Hamiltonians

Abstract

Analytic energy bounds for N-boson systems governed by semirelativistic Hamiltonians of the form H=\sum_{i=1}^N(p_i^2 + m^2)^{1/2} - sum_{1=i<j}^N v/r_{ij}, with v>0, are derived by use of Jacobi relative coordinates. For gravity v=c/N, these bounds are substantially tighter than earlier bounds and they are shown to coincide with known results in the nonrelativistic limit.