论文标题
$ l_ \ infty $ - 编织电动力学的代数
$L_\infty$-algebra of braided electrodynamics
论文作者
论文摘要
使用最近开发的编织非共同场理论的形式主义，我们构建了一个明确的编织电动力学例子，即，与dirac fermion相连的非交换性$ u（1）$量表理论。我们构建了本领域理论的编织的$ l_ \ infty $ - 代数，并应用形式主义以获得运动，动作功能和保守物质当前的编织方程。编织的变形导致电荷保护的修改。最后，计算出对真空极化图的一环贡献中出现的Feynman积分。没有非平面图，但是紫外线/IR混合似乎仍然是。我们评论这个意外的结果。
Using the recently developed formalism of braided noncommutative field theory, we construct an explicit example of braided electrodynamics, that is, a noncommutative $U(1)$ gauge theory coupled to a Dirac fermion. We construct the braided $L_\infty$-algebra of this field theory and apply the formalism to obtain the braided equations of motion, action functional and conserved matter current. The braided deformation leads to a modification of the charge conservation. Finally, the Feynman integral appearing in the one-loop contribution to the vacuum polarization diagram is calculated. There are no non-planar diagrams, but the UV/IR mixing appears nevertheless. We comment on this unexpected result.
