AI 中文总结
本研究针对Veneziano–Vilkovisky超平移相关的软展开结构问题，分析其引出的Kerr多极子生成塔的奇偶交替特性，求解对齐自旋下的全阶结果，最终揭示手征投影后的合成律对应经典$w_{1+\infty}$括号，明确了该代数的物理意义。
AI 中文摘要
Veneziano–Vilkovisky超平移是将标准Bondi参考系与散射体固有参考系联系起来的剩余大微分同胚。我们证明它引出了由指数化软展开筛选的一个塔结构，该对象在三点处生成Kerr多极子。由于$e^{ηωa\cdot q}$可拆分为奇偶两部分，该塔的奇偶性交替变化，对于对齐自旋的情况，我们通过双曲积分求解得到了其所有阶的结果。在手征投影之后，它的合成律就是经典的$w_{1+\infty}$括号：这正是我们赋予该代数的物理内涵。
英文摘要
The Veneziano--Vilkovisky supertranslation is the residual large diffeomorphism relating the canonical Bondi frame to the intrinsic frame of the scattering bodies. We show it leads a tower selected by the exponentiating soft expansion, the object generating the Kerr multipoles at three points. Since \(e^{ηωa\cdot q}\) splits into even and odd parts, the tower alternates parity, and for aligned spin we solve it to all orders in hyperbolic integrals. After a chiral projection its composition law is the classical $w_{1+\infty}$ bracket: the physical content we assign to that algebra.
Comments9 pages, 1 figure + Supplemental Material
