规范切片

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定义 · 14.2 玻色弦的量子理论

按照标准的法捷耶夫-波波夫形式，在定义 $Z_g$ 时必须把这些对称性所对应的自由度去掉。例如，由 $(X_1,{\gamma }_1)$ 与 $(X_2,{\gamma }_2)$ 所指定的弦几何，若二者由 $\mathrm{Diff}({\Sigma }_g)$ 中的某个元素相联系，就不应被独立地计数。同样，$(X,\gamma )$ 与 $(X,{\mathrm{e}}^{\varphi }\gamma )$ 也不应被当作彼此独立的位形。除非特别加以注意，我们就会把同一组位形重复计数无穷多次，从而导致灾难性的发散。事实上，所有几何 $(X,\gamma )$ 构成的空间可以划分成若干等价类（即规范切片(gauge slice)），其中任意两点都不能由这些对称性相联系，如图 14.2所示。

英文原文

According to the standard Faddeev-Popov formalism, the degrees of freedom corresponding to these symmetries have to be omitted when we define $Z_g$ . For example, the string geometry specified by the pairs $(X_1,{\gamma }_1)$ and $(X_2,{\gamma }_2)$ should not be counted independently if they are related by an element of $\mathrm{Diff}({\Sigma }_g)$ . Similarly, $(X,\gamma )$ and $(X,{\mathrm{e}}^{\varphi }\gamma )$ should not be counted as independent configurations. Unless special attention is paid, we would count the same configurations infinitely many times, which leads to disastrous divergences. It turns out that the space of all the geometries $(X,\gamma )$ can be separated into equivalence classes (the gauge slice), any two points of which cannot be connected by these symmetries, see figure 14.2.

出处：14.2 玻色弦的量子理论 · node a-4ce4dd672c8cac89692876f2 · 源节点 SHA-256 bd6a98de90aac822…