论文标题
Cauchy数据空间和共形经典田地理论的多链公式
Cauchy data space and multisymplectic formulation of conformal classical field theories
论文作者
论文摘要
在本文中，我们以局部形式的行为来检查古典田地理论的动态。我们对多核设置的兴趣来自其对现场理论的适当描述，并且已添加了保形性特征来说明比例不变的场理论，并且因为可以精确地解决或分类某些共形场。特别是，我们将使用几何汉密尔顿 - 雅各比理论来解决保形标量场的示例，该理论明确提出了在多胶状歧管上的共形场。为了完成研究田间理论的几何方法，我们提出了汉密尔顿 - 雅各比理论，用于在库奇数据空间中分别分别分开时空和时间在cauchy数据空间中的保形场，并在无限二维流形中描述了动力学。
In this article we inspect the dynamics of classical field theories with a local conformal behavior. Our interest in the multisymplectic setting comes from its suitable description of field theories, and the conformal character has been added to account for field theories that are scale invariant, flat spaces, and because some conformal fields can be exactly solved or classified. In particular, we will solve the example of a conformal scalar field using the geometric Hamilton-Jacobi theory that is explicitly proposed for conformal fields on a multisymplectic manifold. To complete the geometric approach to study field theories, we propose the Hamilton-Jacobi theory for conformal fields in a Cauchy data space, in which space and time are split separately and the dynamics is depicted in an infinite-dimensional manifold.
