论文标题
在晶格上的玻色子场理论的整合性和散射
Integrability and scattering of the boson field theory on a lattice
论文作者
论文摘要
晶格上的免费玻色子是人们可以想到的最简单的田间理论。它的分区功能可以轻松地在动量空间中计算。但是，这种直接的解决方案隐藏了其可集成性属性。在这里，我们使用了当前适用于自旋系统的准确可解决模型的方法，这些模型可用于2D晶格上的无质量且巨大的玻色子。该模型的玻尔兹曼权重显示可满足杨巴克斯特方程，并在无质量的情况下由三角函数给出均匀化，在大规模的情况下雅各比椭圆形函数。我们将行对行传输矩阵对角线，得出保守的数量，并实现量子逆散射方法。最后，我们使用三角和椭圆函数构建了两个分解的散射$ s $矩阵模型，以连续自由度。这些结果将自由玻色子模型置于2D位置与其他模型相同的位置，这些模型完全可以解决，Yang-baxter可以在量子计算中提供可能的应用。
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of exactly solvable models, that are currently applied to spin systems, to a massless and massive free boson on a 2D lattice. The Boltzmann weights of the model are shown to satisfy the Yang-Baxter equation with a uniformization given by trigonometric functions in the massless case, and Jacobi elliptic functions in the massive case. We diagonalize the row-to-row transfer matrix, derive the conserved quantities, and implement the quantum inverse scattering method. Finally, we construct two factorized scattering $S$ matrix models for continuous degrees of freedom using trigonometric and elliptic functions. These results place the free boson model in 2D in the same position as the rest of the models that are exactly solvable à la Yang-Baxter, offering possible applications in quantum computation.
