三角格点上的量子布朗运动与费米-玻色等价：边界态公式的应用
Quantum Brownian Motion on a Triangular Lattice and Fermi-Bose Equivalence: An Application of Boundary State Formulation
摘要：
讨论了三角晶格上量子布朗运动的玻色-费米等价性，将量子布朗运动的作用量映射为具有周期边界快子势的弦论作用量.本文构造了一种新的Klein因子，它比传统的Klein因子更适合于处理二维有边界时空上的量子场论.利用费米-玻色等价和新的Klein因子，我们证明了三角晶格上量子Bownian运动的模型在非临界区等价于边界项为二次费米子场算符的Thirring模型，在临界点等价于边界项为二次费米子场算符的$SU(3)\times SU(3)$自由费米子理论.
英文摘要：
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.
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