Jackura, A. W.Dawid, S. M.Fernández Ramírez, CésarMathieu, V.Mikhasenko, M.Pilloni, A.Sharpe, S. R.Szczepaniak, A. P.2024-12-042024-12-042019-08-13Jackura, Dawid, Fernández-Ramírez, Mathieu, Mikhasenko, Pilloni, Sharpe, & Szczepaniak. (2019). Equivalence of three-particle scattering formalisms. Physical Review D, 100(3). https://doi.org/10.1103/PHYSREVD.100.0345082470-0029, 2470-0010https://doi.org/10.1103/PhysRevD.100.034508https://hdl.handle.net/20.500.14468/24694The registered version of this article, first published in “Physical Review D, 100(3)", is available online at the publisher's website: American Physical Society, https://doi.org/10.1103/PhysRevD.100.034508La versión registrada de este artículo, publicado por primera vez en “Physical Review D, 100(3)", está disponible en línea en el sitio web del editor: American Physical Society, https://doi.org/10.1103/PhysRevD.100.034508In recent years, different on-shell 𝟑→𝟑 scattering formalisms have been proposed to be applied to both lattice QCD and infinite-volume scattering processes. We prove that the formulation in the infinite volume presented by Hansen and Sharpe in [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015).] and subsequently Briceño et al. in [R. A. Briceño, M. T. Hansen, and S. R. Sharpe, Phys. Rev. D 95, 074510 (2017).] can be recovered from the 𝐵-matrix representation, derived on the basis of 𝑆-matrix unitarity, presented by Mai et al. in [M. Mai, B. Hu, M. Döring, A. Pilloni, and A. Szczepaniak, Eur. Phys. J. A 53, 177 (2017).] and Jackura et al. in [A. Jackura, C. Fernández-Ramírez, V. Mathieu, M. Mikhasenko, J. Nys, A. Pilloni, K. Saldaña, N. Sherrill, and A. P. Szczepaniak (JPAC Collaboration), Eur. Phys. J. C 79, 56 (2019).] Therefore, both formalisms in the infinite volume are equivalent and the physical content is identical. Additionally, the Faddeev equations are recovered in the nonrelativistic limit of both representations.eninfo:eu-repo/semantics/openAccessartículo