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Relating The Finite-Volume Spectrum And The Two And Three-Particle S Matrix For Relativistic Systems Of Identical Scalar Particles, Raúl Briceño, Maxwell T. Hansen, Stephen R. Sharpe

Physics Faculty Publications

Working in relativistic quantum field theory, we derive the quantization condition satisfied by coupled two- and three-particle systems of identical scalar particles confined to a cubic spatial volume with periodicity L. This gives the relation between the finite-volume spectrum and the infinite-volume 2 → 2, 2 → 3, and 3 → 3 scattering amplitudes for such theories. The result holds for relativistic systems composed of scalar particles with nonzero mass m, whose center of mass energy lies below the four-particle threshold, and for which the two-particle K matrix has no singularities below the three-particle threshold. The quantization condition is exact …