Speaker
Description
We provide the generalization of the formalism needed to relate the three-particle
finite-volume spectrum to infinite-volume scattering amplitudes for the case of three nondegenerate scalar particles with arbitrary masses. The results can be expressed in a form similar to those for identical particles, except for the addition of an extra flavor index. We do so using a simplified method in which one first works in time-ordered perturbation theory, and obtains a three-particle quantization condition involving a three-particle kernel whose nine flavor-matrix entries correspond to different subclasses of diagrams. The second stage uses symmetrization identities to rewrite the quantization condition in a form with a single three-particle kernel that sums all diagrams and is Lorentz invariant. The relation of these kernels to the infinite-volume scattering amplitude is also given. A third form of the formalism, which is explicitly Lorentz invariant at every stage, is also derived using Feynman diagrams.
