Alternative derivation of the relativistic three-particle quantization condition

Understand

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 $\mathbb Z_2$ symmetry.

• The simplification is afforded by using a three-particle quasilocal K matrix that is not fully symmetrized, $\widetilde{\mathcal{K}}_{\rm df,3}^{(u,u)}$, 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, $\mathcal{K}_{\rm df,3}$.