Equivalence of relativistic three-particle quantization conditions

We show that a recently derived alternative form of the relativistic three-particle quantization condition for identical particles can be rewritten in terms of the R matrix introduced to give a unitary representation of the infinite-volume three-particle scattering amplitude. Combined with earlier work, this shows the equivalence of the relativistic effective field theory approach of Refs. [M. T. Hansen and S. R. Sharpe, Phys. Rev. D 90, 116003 (2014); M. T. Hansen and S. R. Sharpe, Phys. Rev. D 92, 114509 (2015)] and the "finite-volume unitarity" approach of Refs. [M. Mai and M. Doring, Eur. Phys. J. A 53, 240 (2017); M. Mai and M. Doring, Phys. Rev. Lett. 122, 062503 (2019)]. It also provides a generalization of the latter approach to arbitrary angular momenta of two-particle subsystems.