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

TL;DR

This paper explores the Bose-Fermi equivalence in quantum Brownian motion on a triangular lattice by mapping it to string theory and using new Klein factors, revealing its equivalence to boundary Thirring and free fermion models.

Contribution

It introduces new Klein factors for boundary quantum field theories and demonstrates the equivalence of quantum Brownian motion on a triangular lattice to boundary Thirring and free fermion models.

Findings

Model equivalent to boundary Thirring model off-critical regions.

At critical point, model maps to $SU(3)\times SU(3)$ free fermion theory.

New Klein factors improve boundary quantum field theory formulations.

Abstract

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.