  Relativistic world-line Hamiltonian for strongly interacting 3q systems in
magnetic field is derived from the path integral for the corresponding Green's
function. The neutral baryon Hamiltonian in magnetic field obeys the
pseudomomentum conservation and allows a factorization of the c.m. and internal
motion. The resulting expression for the baryon mass in magnetic field is
written explicitly with the account of hyperfine, OPE and OGE (color Coulomb)
interaction. The neutron mass is fast decreasing with magnetic field, losing
1/2 of its value at eB~0.25 GeV^2 and is nearly zero at eB~0.5 GeV^2. Possible
physical consequences of the calculated mass trajectory of the neutron, M_n(B),
are presented and discussed.
