高自旋理论中的微分收缩同伦
Differential Contracting Homotopy in Higher-Spin Theory
AI总结：
本文提出一种处理非线性高自旋方程的新方法，将顶点重构映射为多面体上同调，简化计算并避免Schouten恒等式，可重现并扩展低阶顶点结果。
摘要：
本文发展了一种分析非线性高自旋方程的新高效方法，该方法在处理高自旋理论非线性顶点中的辅助旋量变量$Z_A$与积分同伦参数时采取民主处理方式。所提出的方法最为一般，同时比现有方法简单得多，尤其无需使用Schouten恒等式。值得注意的是，高自旋顶点的重构问题被映射为以同伦参数自身定义的某种多面体上同调。新方案为研究高自旋理论中的高阶修正，特别是其自旋局域性，提供了强大工具。通过对低阶顶点的分析加以说明，不仅重现了先前通过平移同伦方法获得的结果，还得到了在该方案中此前无法触及的、具有最少导数数目的射影紧致顶点。
英文摘要：
A new efficient approach to the analysis of nonlinear higher-spin equations, that treats democratically auxiliary spinor variables $Z_A$ and integration homotopy parameters in the non-linear vertices of the higher-spin theory, is developed. Being most general, the proposed approach is the same time far simpler than those available so far. In particular, it is free from the necessity to use the Schouten identity. Remarkably, the problem of reconstruction of higher-spin vertices is mapped to certain polyhedra cohomology in terms of homotopy parameters themselves. The new scheme provides a powerful tool for the study of higher-order corrections in higher-spin theory and, in particular, its spin-locality. It is illustrated by the analysis of the lower order vertices, reproducing not only the results obtained previously by the shifted homotopy approach but also projectively-compact vertices with the minimal number of derivatives, that were so far unreachable within that scheme.
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