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

Quantum Brownian Motion on a Triangular Lattice and Fermi-Bose Equivalence: An Application of Boundary State Formulation