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...
- 物理角度：Chern-Simons theory 是一个三维的拓扑量子场论，它以 Chern-Simons form 作为作用量，描...
The Chern–Simons form [ 1 , 2 , 3 ] is defined as where k is the Cartan homotopy operator in the case ...doi:10.1007/1-4020-4522-0_93Pablo MoraSpringer Netherlands
We consider a group G with generators T I, the gauge potential 1-form [equation] and the curvature 2-form F = dA + A2, defined on a manifold M2 N + 2 of even dimension 2 N+ 2. The covariant...Connes, AlainWit, Bernard de...
For any G-invariant polynomial P, the transgressive forms $TP(omega)$ defined by Chern and Simons in (Ann. Math. 99:48–69, 1974) are shown to extend to forms $Phi P(omega)$ on associated bundles B with fiber a quotient F = G/H of the group. These forms satisfy a heterotic ...
Forms of Chern-Simons type associated to homogeneous pseudo-Riemannian structures are considered. The corresponding secondary classes are a measure of the lack of a homogeneous pseudo-Riemannian space to be locally symmetric. Explicit computations are done for some pseudo-Riemannian Lie groups and their...
因此Chern-Simons泛函的临界点正是平坦联络.这也是Chern-Simons理论优美的地方，因为平坦联络实际上对对应...
陈-西蒙斯理论（Chern-Simons theory）由陈省身和詹姆斯·西蒙斯所提出的一种规范理论。它是关于在三维底...
The minimal actions of the Lagrangian formulation which satisfy the master equation of Batalin and Vilkovisky have the same Chern-Simons form as the starting classical actions. In the Hamiltonian formulation we have used the formulation of cohomological perturbation and explicitly show that the gauge...
2.1The Chern–Simons gravity The Lovelock action is a polynomial of degree[d/2]in curvature, which can be written in terms of the Riemann curvature and the vielbeine^{a}in the form of (1) and (2). In the first order formalism the Lovelock action is regarded as a functional of the...