高维阿贝尔规范场的重整化流不动点
Renormalization flow fixed points for higher-dimensional abelian gauge fields
摘要：
平凡主丛$M\times G$上的联络模规范对称是从$M$的环群到$G$的态射。因此，只考虑围绕$M$上一个著名的逐步细化胞腔结构族的2-胞腔的循环，阿贝尔规范场的可观测代数$A$可以表示为多项式代数的导数的归纳极限.在这种情况下，球面上杨-米尔斯场的态$μ_λ:A\rightarrow\mathbb{C}$可以写成$μ_λ= μ_0\mathrm{e}^{λL}$，其中$λ$是相互作用强度参数，$L:A\rightarrow A$是显式二阶偏微分算子，$μ_0$是几乎必然平坦连接的态。外推，我们提供了类似的状态的情况下，交换规范场的$\mathbb{R}^d$。
英文摘要：
A connection modulo gauge symmetry on the trivial principal bundle $M\times G$ is a morphism from the loop group of $M$ into $G$. Thus, considering only loops around the 2-cells of a distinguished family of progressively refined cellular structures on $M$, the observable algebra $A$ of an abelian gauge field can be presented as an inductive limit of quotients of polynomial algebras. In that context, it turns out that the state $μ_λ:A\rightarrow\mathbb{C}$ of the Yang-Mills field on the sphere can be written $μ_λ= μ_0\mathrm{e}^{λL}$ with $λ$ an interaction strength parameter, $L:A\rightarrow A$ an explicit second-order partial differential operator and $μ_0$ the state of an almost surely flat connection. Extrapolating, we provide analogous states for the case of abelian gauge fields on $\mathbb{R}^d$.
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