A relativistic, model-independent, three-particle quantization condition

Understand

We present a generalization of Luescher's relation between the finite-volume spectrum and scattering amplitudes to the case of three particles.

• We consider a relativistic scalar field theory in which the couplings are arbitrary aside from a Z2 symmetry that removes vertices with an odd number of particles.
• The theory is assumed to have two-particle phase shifts that are bounded by \pi/2 in the regime of elastic scattering.
• We determine the spectrum of the finite-volume theory from the poles in the odd-particle-number finite-volume correlator, which we analyze to all orders in perturbation theory.