The energy of a system of relativistic massless bosons bound by oscillator pair potentials

TL;DR

This paper derives precise bounds for the ground state energy of a relativistic system of massless bosons interacting via quadratic pair potentials, providing highly accurate estimates across different particle numbers.

Contribution

It establishes tight inequalities for the lowest energy of a semirelativistic bosonic system with quadratic interactions, improving understanding of such quantum systems.

Findings

Derived bounds for the energy with less than 0.15% error for all N>1

Explicit constants A and B define the energy bounds

The bounds scale with [g N^2 (N-1)^2]^{1/3}

Abstract

We study the lowest energy E of a semirelativistic system of N identical massless bosons with Hamiltonian H= sum{i=1 to N} sqrt(p_i^2)+ sum{j>i=1 to N} g |r_i - r_j|^2, g > 0. We prove the inequalities A [g N^2 (N-1)^2]^{1/3} < E < B [g N^2 (N-1)^2]^{1/3}, where A = 2.33810741 and B = [81/(2 pi)]^{1/3} = 2.3447779. The average of these bounds determines E with an error less than 0.15% for all N > 1.