  We discuss the Bose-Fermi equivalence in the quantum Brownian motion (QBM) on
a triangular lattice, mapping the action for the QBM into a string theory
action with a periodic boundary tachyon potential. We construct new Klein
factors which are more appropriate than the conventional ones to deal with the
quantum field theories defined on a two dimensioanl space-time with boundaries.
Using the Fermi-Bose equivalence with the new Klein factors, we show that the
model for the quantum Bownian motion on a triangular lattice is equivalent to
the Thirring model with boundary terms, which are quadratic in fermion field
operators, in the off-critical regions and to a $SU(3)\times SU(3)$ free
fermion theory with quadratic boundary terms at the critical point.
