论文标题
运动振幅和形式因素的运动型HOPF代数
Kinematic Hopf algebra for amplitudes and form factors
论文作者
论文摘要
我们为Yang-Mills理论中的树级振幅和形式的伯尔尼 - 卡拉斯科 - 约翰逊（BCJ）分子提出了一个运动代数，并结合了双性异会标量。代数的代数发生器包含两个部分：第一部分仅仅是双聚体标量的风味因子，第二部分是映射到BCJ Nemerators的非平凡运动学结构的第二部分。基础运动代数使我们能够为BCJ分子提供任何数量的胶子和两个或两个或更多标量的封闭形式，用于壳振幅幅度和涉及外壳操作员的形态。以这种方式构建的BCJ分子显然是不变的，并遵守了从运动代数继承的许多新型关系。
We propose a kinematic algebra for the Bern-Carrasco-Johansson (BCJ) numerators of tree-level amplitudes and form factors in Yang-Mills theory coupled with bi-adjoint scalars. The algebraic generators of the algebra contain two parts: the first part is simply the flavour factor of the bi-adjoint scalars, and the second part that maps to non-trivial kinematic structures of the BCJ numerators obeys extended quasi-shuffle fusion products. The underlying kinematic algebra allows us to present closed forms for the BCJ numerators with any number of gluons and two or more scalars for both on-shell amplitudes and form factors that involve an off-shell operator. The BCJ numerators constructed in this way are manifestly gauge invariant and obey many novel relations that are inherited from the kinematic algebra.
