论文标题
U（1）晶格模型的弱耦合极限为傅立叶
Weak Coupling Limit of U(1) Lattice Model in Fourier Basis
论文作者
论文摘要
U（1）晶格模型的转移矩阵在傅立叶基础上和弱耦合极限中考虑。高斯法律约束和规格不变状态的问题以傅立叶为基础解决。特别是，在强耦合限制的情况下，量规傅立叶状态实际上是有限尺寸的闭环电流。然而，在弱耦合极限中，沿周期性或无限空间方向的链路电流与规格不变状态相当。讨论了与在傅立叶基础上转移矩阵极端弱耦合有关的微妙之处。对二次操作中矩阵的零特征值的仔细分析导致在限制$ g \至0 $中安全提取不同的组体积。通过晶格模型的非常基本的概念和工具，分析得出了任何晶格的任何维度和大小的弱耦合极限的光谱。弱耦合极限处的频谱在较大的晶格极限中与连续模型相对应。
The transfer-matrix of the U(1) lattice model is considered in the Fourier basis and in the weak coupling limit. The issues of Gauss law constraint and gauge invariant states are addressed in the Fourier basis. In particular, it is shown that in the strong coupling limit the gauge invariant Fourier states are effectively the finite size closed loop currents. In the weak coupling limit, however, the link-currents along periodic or infinite spatial directions find comparable roles as gauge invariant states. The subtleties related to the extreme weak coupling of the transfer-matrix in the Fourier basis are discussed. A careful analysis of the zero eigenvalues of the matrix in the quadratic action leads to a safe extraction of the diverging group volume in the limit $g\to 0$. By means of the very basic notions and tools of the lattice model, the spectrum at the weak coupling limit for any dimension and size of lattice is obtained analytically. The spectrum at the weak coupling limit corresponds to the expected one by the continuum model in the large lattice limit.
