论文标题
深色田地确实存在于Weyl几何形状中
Dark Fields do Exist in Weyl Geometry
论文作者
论文摘要
广义的Weyl积分几何形状（GWIG）是从A（伪） - 里曼尼亚歧管的切线和cotangent束的同时仿射变换获得的。与经典的Weyl综合几何形状（CWIG）相比，这里有两个概括：与任意黑场的相互作用，以及各向异性扩张。这意味着CWIG已经与{\ it null}黑暗字段具有相互作用。 GWIG可以解决一些经典的数学和物理问题。例如，通过衍生麦克斯韦方程及其子集的推导，Gwig上的保护，双曲线和椭圆方程；我们与任意黑暗场进行了互动。此外，通过使用类似于Penrose共形无穷大的概念，可以在这些方程式上施加边界条件。作为一个很好的例子，我们为椭圆方程而做到了这一点，在那里我们获得了无奇异的潜在理论。然后，我们将这种潜在理论用于构造点带电粒子的非单明模型。它解决了经典真空状态的无限能量的难度。
A generalized Weyl integrable geometry (GWIG) is obtained from simultaneous affine transformations of the tangent and cotangent bundles of a (pseudo)-Riemannian manifold. In comparison with the classical Weyl integrable geometry (CWIG), there are two generalizations here: interactions with an arbitrary dark field, and, anisotropic dilation. It means that CWIG already has interactions with a {\it null} dark field. Some classical mathematics and physics problems may be addressed in GWIG. For example, by derivation of Maxwell's equations and its sub-sets, the conservation, hyperbolic, and elliptic equations on GWIG; we imposed interactions with arbitrary dark fields. Moreover, by using a notion analogous to Penrose conformal infinity, one can impose boundary conditions canonically on these equations. As a prime example, we did it for the elliptic equation, where we obtained a singularity-free potential theory. Then we used this potential theory in the construction of a non-singular model for a point charged particle. It solves the difficulty of infinite energy of the classical vacuum state.
