  We derived the corresponding boundary condition on Fermi fields to the
spin-1/2 Heisenberg chain with boundary magnetic fields. In order to obtain the
correct boundary condition from the variation of the action at the edges, we
carefully treat the oscillating terms which emerge as a result of the chiral
decomposition of fermions and do not contribute to the bulk Lagrangian. The
obtained result is checked by compared with the exact result derived from the
Bethe ansatz, by considering the mode expansion of fermions on the light-cone
coordinates. We also give the spin-wave interpretation to the emergence of
boundary bound states.
