发表机构
ENEA, Nuclear Department, Frascati Research Center（意大利国家新能源与可持续经济署，核能部，弗拉斯卡蒂研究中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文利用高阶Hermite-Kampé de Fériet多项式统一构造典型突变积分的影子表示，并通过解析影子框架处理欧几里得Pearcey核，确立了积分与解析求值的交换。
AI 中文摘要
高阶多变量Hermite-Kampé de Fériet多项式为典型突变积分的影子表示提供了统一构造。将这些多项式展开展开指数，并针对主突变核进行积分，在合适的衰减轮廓上给出收敛的矩展开。一个通用的形式影子算子随后通过显式矩基态表达所得场。我们针对折叠、尖点和燕尾突变发展了此构造，并将欧几里得Pearcey场与四次标量配分函数联系起来。当积分在影子求值之前进行时，形式与解析影子框架之间的区别变得至关重要。对于欧几里得Pearcey，积分后的线性化核是一个有理函数，其作用未由原始形式规则指定。解析影子框架为该核提供了收敛的Mellin配对，并恢复了独立获得的二元Pearcey表示。这在此例中确立了积分与解析求值的交换，并识别了形式框架之外的具体扩展。
英文摘要
Higher-order multivariable Hermite-Kampé de Fériet polynomials provide a unified construction of umbral representations for canonical catastrophe integrals. Expanding the unfolding exponential in these polynomials and integrating against the leading catastrophe kernel gives convergent moment expansions on suitable decay contours. A universal formal umbral operator then expresses the resulting fields through explicit moment ground states. We develop this construction for the fold, cusp and swallowtail, and relate the Euclidean Pearcey field to quartic scalar partition functions. The distinction between formal and analytic umbral frameworks becomes essential when integration is performed before umbral evaluation. For Euclidean Pearcey, the integrated linearized kernel is a rational function whose action is not specified by the original formal rules. The Analytic Umbral Framework supplies a convergent Mellin pairing for this kernel and recovers the independently obtained bivariate Pearcey representation. This establishes, in this example, an exchange of integration and analytic evaluation and identifies a specific extension beyond the formal framework.
Comments23 pages
