Physical Review D
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 up to corrections of the order 𝒪 (e−mL)and holds for any choice of total momenta satisfying the boundary conditions.
Original Publication Citation
Briceño, R.A., Hansen, M.T., Sharpe, S.R. (2017) Relating the finite-volume spectrum and the two-and-three particle S matrix for relativistic systems of identical scalar particles. Physical Review D, 95(7), 1-40, Article 074510. https://doi.org/10.1103/PhysRevD.95.074510
Briceño, Raúl; Hansen, Maxwell T.; and Sharpe, Stephen R., "Relating the Finite-Volume Spectrum and the Two and Three-Particle S Matrix for Relativistic Systems of Identical Scalar Particles" (2017). Physics Faculty Publications. 627.