2017/01/31 by Raúl A. Briceño, Maxwell T. Hansen, Stephen R. Sharpe · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boson #Finite volume method #Geometry #Gravitational singularity #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantization (signal processing) #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Scalar (mathematics) #Scalar boson #Scalar field #Statistics #hep-lat #nucl-th
paper · pdf · doi:10.1103/physrevd.95.074510
published as Phys. Rev. D 95, 074510 (2017) · 47 pages, 19 figures
openalex created_date 2017/02/10 · openalex publication_date 2017/04/18 · arxiv created 2017/04/30 · arxiv updated 2017/05/02 · openalex updated_date 2026/08/05
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\ensuremath→2, 2\ensuremath→3, and 3\ensuremath→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^\ensuremath-mL) and holds for any choice of total momenta satisfying the boundary conditions.