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

Richard L. Hall·Wolfgang Lucha·Franz F. Schoeberl
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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.

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Richard L. Hall, Wolfgang Lucha, Franz F. Schoeberl. 2003-11-20. The energy of a system of relativistic massless bosons bound by oscillator pair potentials. https://doi.org/10.1016/j.physleta.2003.11.019

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