Alternative derivation of the relativistic three-particle quantization condition

We present a simplified derivation of the relativistic three-particle quantization condition for identical, spinless particles described by a generic relativistic field theory satisfying a Z(2) symmetry. The simplification is afforded by using a three-particle quasilocal K matrix that is not fully symmetrized, (K) over bar ((u,u))(df,3) and makes extensive use of time-ordered perturbation theory (TOPT). We obtain a new form of the quantization condition. This new form can then be related algebraically to the standard quantization condition, which depends on a fully symmetric three-particle K matrix, K-df,K- 3. The new derivation is fully explicit, allowing, for example, a closed-form expression for K-df,K- 3 to be given in terms of TOPT amplitudes. The new form of the quantization condition is similar in structure to that obtained in the "finite-volume unitarity" approach, and in a companion paper we make this connection concrete. Our simplified approach should also allow a more straightforward generalization of the quantization condition to nondegenerate particles, and perhaps also to more than three particles.