Speaker
Description
Recent years have witnessed a rapid growth of interest to the three-body
problem on the lattice. In this connection, the derivation of a relativistic-
invariant three-particle quantization condition, which relates the finite-volume
lattice spectrum to the infinite-volume observables in the three-particle sec-
tor, has become a major challenge. First and foremost, providing a manifestly
relativistic-invariant framework is important because the typical momenta of
light particles studied on the lattice are generally not small, as compared to
their mass. Moreover, Lorentz invariance puts stringent constraints on the
possible form of the two- and three-body interactions, reducing the number
of effective couplings needed for their parameterization. These constraints
are absent in the non-invariant formulations, leading to an inflation of the
number of independent parameters.
In the literature, there exist three different but conceptually equivalent
formulations of the three-particle quantization condition. In this talk, I shall
put the issue of the relativistic covariance of these formulations under a
renewed scrutiny. A novel formulation is suggested, which is devoid of some
shortcomings of the existing approaches related to the explicit non-covariance
of the three-particle propagator. The proposed approach is based on the
“covariant” NREFT framework. We reformulate this framework, choosing
the quantization axis along an arbitrary timelike unit vector vμ, demonstrate
the explicit relativistic invariance of the infinite-volume Faddeev equations
and derive the modified quantization condition. The relativistic invariance is
tested numerically, producing synthetic data for the energy levels in different
moving frames.
