换句话说,积掉[18]Chern-Simons规范场为每次交换插入相位 e^{\pm i\vartheta} ,给出分数统计。 真空Abel Chern-Simons理论 4.3节已经指出,任意子理论的真空知道粒子的统计,即使是在粒子还没有出现的时候。[19]也就是说,环面上的基态简并度与粒子种数匹配。那么,没有粒子时,我们关心...
在Chern-Simons理论中,Chern-Simons形式的一般定义为:\[ CS(A) = \text{Tr}\left(A \wedge dA + \frac{2}{3}A \wedge A \wedge A\right) \]在我们的场景中,联络A的数学表达式为\(A = v \cdot \cos(\theta) d\phi\),而曲率F的数学表达式为\(F = -v \cdot \sin(\theta) d\theta \wed...
$\textbf{Chern-Simons形式与拓扑场论}$ Chern-Simons场论是一种的拓扑场论，亦是一种规范场论。实际上规范理论在学习电动力学时候就有所接触，实际上电磁理论就是最简单的规范场论，电磁场是$U(1)$纤维丛上的联络（注意与广义相对论不同的是，引力场是Riemann流形上的联络）。在这上面构造一个拓扑不变量的...
This is the Chern–Simons pre-quantization of moduli spaces. The group of gauge transformations on the boundary of the four-manifold acts on the moduli space of flat connections by an infinitesimally symplectic way. When the four-manifold is a 4-dimensional disc we show that this action is ...
If Chern–Simons theory is the appropriate odd- dimensional gauge theory and if Born–Infeld theory is the appropriate even-dimensional theories to provide a framework for the gravitational interaction, then these theories must satisfy the correspondence principle, namely they must be related to general...
Chern-Simons-Higgs薛定铐方程组解的存在性 邓金 (江西师范大学数学与统计学院南昌330022)摘要：对于含有中性标量场及规范位势的非线性薛定谭方程组，当非线性项的增长指数p>2时，该文证明了非平凡解的存在性.关键词：薛定谭方程；中性标量场；Chern-Simons.MR(2010)主题分类：35J20;35Q40;35Q51中图分类号：...
The boundary of the 3-brane is described by a Chern-Simons 2-brane. We identify the bulk of the 3-brane with the interior of a hadronic bag and the world-volume of the Chern-Simons 2-brane with the dynamical boundary of the bag. We estimate the value of the induced bag constant to...
Chern-Simons theory can be defined on a cell complex, such as a network of bubbles, which is not a (Hausdorff) manifold. Requiring gauge invariance determines the action, including interaction terms at the intersections, and imposes a relation between the coupling constants of the CS terms on ...
首先,咱们先把Chern-Simons理论的这个拉格朗日量给写出来,这个理论要包含一个特殊的矢量场或者说是矢势aα,就类似于电磁矢势Aα那样,不过注意这只是个类比而已。然后,要想搞出来符合前面讲述的那种任意子,我们还记得,空间得是个二维空间。所以,我们就大概知道要写一个二维的关于矢势aα的理论:...