AI 中文总结
该研究发展经典散射的相空间描述，通过部分Weyl变换Dyson S矩阵的物质部分，将包容波形、相空间位移等经典可观测量关联为同一S矩阵符号的不同投影，还导出非线性引力记忆与量子几何，阐明其在标量QED和引力中的静场效应。
AI 中文摘要
我们发展了经典散射的相空间描述，其中Dyson S矩阵的物质部分经过部分Weyl变换，而辐射部分仍为算符值。所得S矩阵符号为若干经典可观测量提供了共同起源：我们证明，包容波形、相空间中的经典位移（即冲量与位置偏移）以及角动量均源自同一对象的不同投影。我们表明，部分Weyl变换后的S矩阵可按弹性相位与连通辐射核作指数组织，而其包容单投影具有相干代表，其波形α_I描述经典辐射，扩展了我们近期的提议。此外，我们明确展示了如何从包容相干波形导出非线性引力记忆。波形对硬散射数据的依赖自然产生量子几何，包括波形空间上的诱导Berry联络，其对相空间位移的贡献同时包含辐射反作用与静场效应。我们通过推导标量QED和引力中位置偏移与场角动量的静场贡献，阐明了该结构。
英文摘要
We develop a phase-space description of classical scattering in which the matter sector of the Dyson S-matrix is partially Weyl transformed while the radiation sector remains operator valued. The resulting S-matrix symbol provides a common origin for several classical observables: we show that the inclusive waveform, the classical displacement in phase-space (i.e. the impulse and position shift), and the angular momentum arise as different projections of the same object. We show that the partially Weyl-transformed $S$-matrix admits an exponential organisation in terms of an elastic phase and connected radiation kernels, while its inclusive one-point projection admits a coherent representative with waveshape $α_I$ describing classical radiation, extending our recent proposal. Furthermore, we show explicitly how nonlinear gravitational memory can be derived from an inclusive coherent waveshape. The dependence of the waveshape on the hard scattering data naturally leads to a quantum geometry, including an induced Berry connection on the space of waveforms, whose contribution to the phase-space displacement captures both radiation-reaction and static-field effects. We illustrate this structure by deriving static contributions to the position shift and field angular momentum in both scalar QED and gravity.
