鬼故事III。回到零号幽灵
Ghost story. III. Back to ghost number zero
摘要：
在定义了bc系统的三弦中点插点后，我们分析了gh=0态（楔形态）与gh=3中点插点的关系。我们发现明确的和定期的关系连接两个对象。在楔形态的情况下，这允许我们写下gh=0的诺依曼矩阵的谱分解，尽管它们与K1的矩阵表示不交换。因此，我们追溯这种非对易性的起源是复k平面中楔形本征值的虚极点的结果。有了gh=0和gh=3的显式重建公式，我们终于可以展示中点顶点如何避免gh=0时的固有非对易性，使一切都像零动量物质扇区一样简单。
英文摘要：
After having defined a 3-strings midpoint-inserted vertex for the bc system, we analyze the relation between gh=0 states (wedge states) and gh=3 midpoint duals. We find explicit and regular relations connecting the two objects. In the case of wedge states this allows us to write down a spectral decomposition for the gh=0 Neumann matrices, despite the fact that they are not commuting with the matrix representation of K1. We thus trace back the origin of this noncommutativity to be a consequence of the imaginary poles of the wedge eigenvalues in the complex k-plane. With explicit reconstruction formulas at hand for both gh=0 and gh=3, we can finally show how the midpoint vertex avoids this intrinsic noncommutativity at gh=0, making everything as simple as the zero momentum matter sector.
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