arXiv math/01012072001-01-25math.DGmath.AP

从PDE系统和量子力学到广义域论

From PDE Systems and Metrics to Generalized Field Theories

Constantin Udriste, Mircea Neagu

备注：: The authors express their sincere thanks to Professors V. Balan, V. Obadeanu and D. Opris for their critical reading of an earlier version of this paper
发表信息：: M. Neagu, C. Udriste: "From PDE systems and metrics to multi-time field theories and geometric dynamics", Seminarul de Mecanica 79 (2001), 1-33

摘要：

本文用最小二乘变分方法证明了一阶偏微分方程组的每一个$C^2$ -解，在一阶喷流纤维丛$J^1(T,M)$上，都可以看作是一个“广义调和映射”.我们的思想结构如下：1）我们找到了一个合适的几何结构上的$J^1(T,M)$，将给定的偏微分方程系统的解决方案转化为“广义调和映射”; 2）我们建立了一个自然的几何诱导这样的偏微分方程系统; 3）我们构建了一个域论，在一般的设置，自然地连接到这个偏微分方程系统。

英文摘要：

The paper proved that every $C^2$-solution of a given first order PDEs system, regarded on the jet fibre bundle of order one $J^1(T,M)$, may be viewed as a "generalized harmonic map", via the least squares variational method. Our ideas are structured in the following way: 1) we find a suitable geometrical structure on $J^1(T,M)$ that convert the solutions of the given PDEs system into "generalized harmonic maps"; 2) we build a natural geometry induced by a such PDEs system; 3) we construct a field theory, in a general setting, naturally attached to this PDEs system.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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