论文标题
EYM不变矢量空间中EYM振幅的扩展
Expansion of EYM Amplitudes in Gauge Invariant Vector Space
论文作者
论文摘要
由扩大爱因斯坦 - 杨米尔斯理论的单轨树级幅度扩大到Yang-Mills振幅的BCJ基础的问题，我们提出了规格不变矢量空间中的替代扩展公式。从由动量和极化向量的多项式组成的通用矢量空间开始，我们通过施加规格不变条件的约束来将新的子空间定义为规格不变的矢量空间。为了表征此子空间，我们计算其尺寸并构建从中构建明确的规格基础。我们在规格基础上提出了一个扩展公式，其扩展系数是Yang-Mills振幅的线性组合，表现出两个扩展基础和系数的规格不变性。在Quivers的帮助下，我们通过差分运算符计算扩展系数，并通过几个示例演示了一般的扩展算法。
Motivated by the problem of expanding single-trace tree-level amplitude of Einstein-Yang-Mills theory to the BCJ basis of Yang-Mills amplitudes, we present an alternative expansion formula in the gauge invariant vector space. Starting from a generic vector space consisting of polynomials of momenta and polarization vectors, we define a new sub-space as gauge invariant vector space by imposing constraints of gauge invariant conditions. To characterize this sub-space, we compute its dimension and construct an explicit gauge invariant basis from it. We propose an expansion formula in the gauge invariant basis with expansion coefficients being linear combinations of Yang-Mills amplitude, manifesting the gauge invariance of both expansion basis and coefficients. With help of quivers, we compute the expansion coefficients via differential operators and demonstrate the general expansion algorithm by several examples.
