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We show that a recently derived alternative form of the relativisticthree-particle quantization condition for identical particles can be rewrittenin terms of the R matrix introduced to give a unitary representation of theinfinite-volume three-particle scattering amplitude. Combined with earlierwork, this shows the equivalence of the relativistic effective field theoryapproach of Hansen and Sharpe (Refs.[1,2]) and the "finite-volume unitarity"approach of Mai and D\"oring (Refs.[3,4]). It also provides a generalization ofthe latter approach to arbitrary angular momenta of two-particle subsystems.

Equivalence of relativistic three-particle quantization conditions