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 la Yang–Baxter, offering possible applications in quantum computation.

格子上的自由玻色子是人们能想到的最简单的场论。可以很容易地在动量空间中计算其分配函数。但是，这种简单的解决方案隐藏了其可集成性。在这里，我们使用精确可解模型的方法，这些方法目前应用于自旋系统，用于二维晶格上无质量和无质量的玻色子。该模型的Boltzmann权重显示为满足Yang-Baxter方程，在无质量情况下具有三角函数，在大规模情况下具有Jacobi椭圆函数，具有均匀性。我们将行到行传输矩阵对角化，导出守恒量，并实现量子逆散射方法。最后，我们构造两个因式散射S使用三角函数和椭圆函数的连续自由度矩阵模型。这些结果将自由玻色子模型放置在2D平面中，而其余其余模型完全可以解决la Yang–Baxter的问题，从而为量子计算提供了可能的应用。