论文标题
投影式希尔伯特束的平行运输的非关联磁翻译
Non associative magnetic translations from parallel transport in projective Hilbert bundles
论文作者
论文摘要
具有磁场背景的量子系统中翻译的非缔合性已引起了人们的兴趣，这与$ \ Mathbb {r}^n。$相关的拓扑琐碎的gerbes与$ \ mathbb {r}^n。 dixmier-douady类是$ \ mathrm {h}^3（m，\ mathbb {z}）的元素。但是，在当地的微分形式的$ d = 0,1,2,3 $的情况下，有一个更精细的描述，$ n = 3 $ n = 3 $ n = 3 $ nont = 3 $ nnon zere $ b $ b $ b。在本文中，我们根据圆圈上的$ n $组成费用来研究量子场理论结构。试图将1粒子系统上的翻译组动作提升到第二个量化系统时，就会出现非关联性。
The non-associativity of translations in a quantum system with magnetic field background has received renewed interest in association with topologically trivial gerbes over $\mathbb{R}^n.$ The non-associativity is described by a 3-cocycle of the group $\mathbb{R}^n$ with values in the unit circle $S^1.$ The gerbes over a space $M$ are topologically classified by the Dixmier-Douady class which is an element of $\mathrm{H}^3(M,\mathbb{Z}).$ However, there is a finer description in terms of local differential forms of degrees $d=0,1,2,3$ and the case of the magnetic translations for $n=3$ the 2-form part is the magnetic field $B$ with non zero divergence. In this paper we study a quantum field theoretic construction in terms of $n$-component fermions on a circle. The non associativity arises when trying to lift the translation group action on the 1-particle system to the second quantized system.
