Journal
PHYSICAL REVIEW D
Volume 95, Issue 7, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevD.95.074510
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Funding
- U.S. Department of Energy under Jefferson Science Associates, LLC [DE-AC05-06OR23177]
- U. S. Department of Energy [DE-SC0011637]
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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.
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