论文标题
量子外壳递归关系
Quantum Off-Shell Recursion Relation
论文作者
论文摘要
我们为$ ϕ^{4} $ - 理论和Yang-Mills理论的传统树级递归关系以外的任意循环级散射幅度构建了离子递归关系。我们定义了量子扰动器的扩展，其中包括通过识别外部源来从量子有效的作用形式主义中进行的循环校正。我们的方法清楚地表明了扰动器的扩展如何成为脱壳电流生成函数。我们利用dyson-schwinger方程来推导与环路级散射幅度的任意顺序相关的量子外壳递归关系，而不是在常规扰动方法中使用经典运动方程。我们解决了递归关系，并重现了与$ ϕ^{4} $ - 理论同意的结果。此外，我们通过更换外部源的选择来构建用于计算循环级相关函数的递归。
We construct off-shell recursion relations for arbitrary loop-level scattering amplitudes beyond the conventional tree-level recursion relations for $ϕ^{4}$-theory and the Yang-Mills theory. We define a quantum perturbiner expansion that includes loop corrections from the quantum effective action formalism by identifying the external source. Our method clearly shows how the perturbiner expansion becomes an off-shell current generating function. Instead of using the classical equations of motion in the conventional perturbiner method, we exploit the Dyson-Schwinger equation to derive the quantum off-shell recursion relation to arbitrary order of loop-level scattering amplitudes. We solve the recursion relation and reproduce the results which agree up to one-loop six-point scattering amplitudes for $ϕ^{4}$-theory. Furthermore, we construct the recursions for computing loop-level correlation functions by replacing the choice of the external source.
