通过Stratonovich-Weyl对应从量子场论得到经典动力学
Classical dynamics from QFT via Stratonovich-Weyl correspondence
AI总结：
该研究通过Stratonovich-Weyl对应开发从S矩阵提取相对论经典动力学的形式体系，结合S矩阵指数形式得到含Magnus振幅的嵌套括号，可应用于引力波物理。
AI中文摘要：
我们开发了一种从S矩阵中提取相对论经典动力学的形式体系，其中大质量物体在相空间中描述，而无质量辐射则保留在福克空间中。我们的形式体系依赖于量子力学的算符表述与相空间表述之间的Stratonovich-Weyl（SW）对应，该对应由SW量化器协变实现。对于局域入射态，经典可观测量由适当算符的SW符号在入射渐近轨迹上的取值给出。结合S矩阵的指数形式，这些可观测量自然由包含Magnus振幅的嵌套混合狄拉克/对易子括号给出。Magnus振幅是S矩阵对数的矩阵元，我们提供了一种直接算法，用于计算控制 retarded传播子在Magnus振幅图中位置的组合Murua系数。该框架非常适合引力波物理应用。
英文摘要：
We develop a formalism for extracting relativistic classical dynamics from the S-matrix, in which massive bodies are described on phase space while massless radiation is kept in the Fock space. Our formalism relies on the Stratonovich-Weyl (SW) correspondence between the operator and phase-space formulations of quantum mechanics, as implemented covariantly by the SW quantizer. For localized incoming states, classical observables are given by SW symbols of the appropriate operators evaluated on incoming asymptotic trajectories. In combination with the exponential form of the S-matrix, the observables are naturally given by nested mixed Dirac/commutator brackets involving Magnus amplitudes. The latter are the matrix elements of the logarithm of the S-matrix, and we provide a straightforward algorithm for computing the combinatorial Murua coefficients that control the placement of retarded propagators inside Magnus-amplitude diagrams. This picture is well-suited for gravitational-wave physics applications.
