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A proposal by L\"uscher enables one to compute the scattering phases ofelastic two-body systems from the energy levels of the lattice Hamiltonian in afinite volume. In this work we generalize the formalism to S--, P-- and D--wavemeson and baryon resonances, and general total momenta. Employing nonvanishingmomenta has several advantages, among them making a wider range of energylevels accessible on a single lattice volume and shifting the level crossing tosmaller values of $m_\pi L$.

Scattering phases for meson and baryon resonances on general moving-frame lattices