Scattering amplitude recursion relations in Batalin-Vilkovisky-quantizable theories
Scattering amplitude recursion relations in Batalin-Vilkovisky-quantizable theories
复制标题
Batalin-Vilkovisky 可量化理论中的散射振幅递推关系
DOI：
10.1103/physrevd.100.045017
复制
发表时间：
2019
影响因子：
5
通讯作者：
Macrelli T
中科院分区：
文献类型：
--
作者：
Macrelli T
杨-米尔斯理论中的树级散射振幅满足由Berends和Giele引起的递推关系，该递推关系产生了著名的最大螺旋违逆振幅的Parke-Taylor公式。我们证明了这种递归关系的起源在Batalin-Vilkovisky （BV）形式主义中变得清晰，它在一个代数中编码了一个场论。在该代数的拟同构类的最小代表的过渡中得到递归关系，称为最小模型。事实上，准同构包含了散射理论的所有信息。正如我们所解释的，这种最小模型的计算很容易在任何可量化的BV理论中进行，这反过来又为其树级散射振幅产生递归关系。
Tree-level scattering amplitudes in Yang-Mills theory satisfy a recursion relation due to Berends and Giele which yields e.g., the famous Parke-Taylor formula for maximally helicity violating amplitudes. We show that the origin of this recursion relation becomes clear in the Batalin-Vilkovisky (BV) formalism, which encodes a field theory in an-algebra. The recursion relation is obtained in the transition to a smallest representative in the quasi-isomorphism class of that-algebra, known as a minimal model. In fact, the quasi-isomorphism contains all the information about the scattering theory. As we explain, the computation of such a minimal model is readily performed in any BV quantizable theory, which, in turn, produces recursion relations for its tree-level scattering amplitudes.