论文标题
更高维ABELIAN仪表场的重新归一化流量固定点
Renormalization flow fixed points for higher-dimensional abelian gauge fields
论文作者
论文摘要
琐碎的主体捆绑包$ m \ times g $上的连接模量量规对称性是$ m $ to $ g $的循环组的形态。因此，考虑到$ m $上逐渐完善的细胞结构的2个细胞周围的环，可观察的代数$ a $ a $ a abelian仪表场可以作为多种代数的商的电感限制。在这种情况下，事实证明，可以写入Yang-Mills字段的状态$μ_λ：a \ rightarrow \ mathbb {c} $可以书写$μ__λ=μ__0\ mathrm {e}^{e}^{λl} $ a $ a flocational unteraction-a互动参数，$： $μ_0$几乎肯定是平坦的连接的状态。推断，我们在$ \ mathbb {r}^d $上为Abelian Gauge字段提供了类似的状态。
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 $\mathbb{R}^d$.
