The Uncertainty of Fluxes
The Uncertainty of Fluxes
复制标题
通量的不确定性
DOI：
10.1007/s00220-006-0181-3
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发表时间：
2006
影响因子：
2.4
通讯作者：
G. Segal
中科院分区：
文献类型：
--
作者：
D. Freed;G. Moore;G. Segal
在普通的量子麦克斯韦理论的自由电磁场，制定了一个弯曲的三维流形，我们观察到，磁通量和电通量不能同时测量。这个测不准原理反映了挠率：通量模挠率可以同时测量。我们还发展了自对偶场的汉密尔顿理论，指出它们是由庞特亚金自对偶上同调理论量子化的，量子希尔伯特空间是分次的，因此通常包含玻色子态和费米子态。值得注意的是，这些想法适用于弦论中的拉蒙-拉蒙场，表明它的K理论类是无法测量的。
In the ordinary quantum Maxwell theory of a free electromagnetic field, formulated on a curved 3-manifold, we observe that magnetic and electric fluxes cannot be simultaneously measured. This uncertainty principle reflects torsion: fluxes modulo torsion can be simultaneously measured. We also develop the Hamilton theory of self-dual fields, noting that they are quantized by Pontrjagin self-dual cohomology theories and that the quantum Hilbert space is $${\mathbb{Z}/2\mathbb{Z}}$$ -graded, so typically contains both bosonic and fermionic states. Significantly, these ideas apply to the Ramond-Ramond field in string theory, showing that its K-theory class cannot be measured.