Poincar\'e invariant calculation of the three-body bound state energy and wave function

The Faddeev equation for the three-body (3B) bound state of a relativistic mass operator (rest-frame Hamiltonian) is solved directly in terms of momentum vectors without employing a partial wave decomposition. The mass operator is a Casimir operator of a dynamical unitary representation of the Poincar\'e group, which ensures the exact relativistic invariance of the theory. The input to the calculations are relativistic off-shell two-body transition matrices. They are constructed to be phase-shift equivalent to corresponding non-relativistic two-body transition matrices using the invariance principle and the first resolvent equation. Our numerical results show that relativistic effects, using the Malfliet-Tjon V interaction, reduce the 3B binding energy by about 3.3\%. We also compare the structure of the relativistic and corresponding non-relativistic wave functions as a function of the Jacobi momentum vectors.