论文标题
混合物的对称性：量规理论的代数
Symmetries from mixtures: an algebra for gauge theories
论文作者
论文摘要
我们在这里提出了向量和标量之间的产品，该产品将它们混合在自己的空间中，并使用想象力将向量之间的几何产物描述为复杂的向量，而不是引入高阶/尺寸矢量对象。这是通过{\ it混合张量}来完成的，该{\ it混合张量}捕获了几何代数的丰富几何形状，并同时使自己自然地放置了张量计算。我们基于以下想法，即可以通过允许基础空间的曲率使函数可区分的函数在较高维度中发展出一个分析性的概念，我们将其称为{\ IT分析曲率}。为了探索这些想法，我们使用它们来得出一些基本法律和物理运营商，尽管这些定律有些略微，但具有引人注目的特征。例如，混合物会产生丰富的对称性，而不会添加尺寸超出熟悉的时空，并且其导数会产生熟悉的量子场关系，其中场电位只是坐标基础的衍生物。物理定律的对称性不是直接来自基础，而是来自它们的混合物。
We present here a product between vectors and scalars that {\it mixes} them within their own space, using imaginaries to describe geometric products between vectors as complex vectors, rather than introducing higher order/dimensional vector objects. This is done by means of a {\it mixture tensor} that captures the rich geometries of geometric algebras, and simultaneously lends itself naturally to tensor calculus. We use this to develop a notion of analyticity in higher dimensions based on the idea that a function can be made differentiable -- in a certain strong sense -- by permitting curvature of the underlying space, and we call this {\it analytic curvature}. To explore these ideas we use them to derive a few fundamental laws and operators of physics which, while considered somewhat lightly, have compelling features. The mixture, for instance, produces rich symmetries without adding dimensions beyond the familiar space-time, and its derivative produces familiar quantum field relations in which the field potentials are just derivatives of the coordinate basis. The symmetries of physical laws are seen to arise not directly from the bases, but from their mixtures.
