论文标题
量子观察值的弱价值图片：量规不变的矢量电势
Weak value picture on quantum observables: gauge-invariant vector potentials
论文作者
论文摘要
坐标转换下的物理量（称为量规不变性）在量子和经典理论中都是理论框架的基础。量规不变数量的发现使量子现象的几何和拓扑解释与浆果相或量子染色体动力学中的夸克和gluon贡献的分离。在这里，以量子几何数量 - 莓连接，相和曲率的示例，我们通过应用“弱值图片”提取了新的量规数量。通过在弱价值的背景下在浆果阶段的推导中采用不同的前和后选择，我们从最初依赖于衡量的浆果连接中得出了衡量不变的矢量电位，并表明获得的矢量电位与投影动量操作员的弱价值相对应。该数量的局部性质以Aharonov-bohm效应的示例证明，证明该规格不变的矢量电位可以解释为磁场中浆果曲率的唯一来源。这种弱价值分解方法将导致从传统上不可观察的数量中提取新的可测量数量。
The conservation of physical quantities under coordinate transformations, known as gauge invariance, has been the foundation of theoretical frameworks in both quantum and classical theory. The finding of gauge-invariant quantities has enabled the geometric and topological interpretations of quantum phenomena with the Berry phase, or the separation of quark and gluon contributions in quantum chromodynamics. Here, with an example of quantum geometric quantities-Berry connection, phase, and curvature-we extract a new gauge-invariant quantity by applying a "weak value picture". By employing different pre- and post-selections in the derivation of the Berry phase in the context of weak values, we derive the gauge-invariant vector potential from the Berry connection that is originally gauge-dependent, and show that the obtained vector potential corresponds to the weak value of the projected momentum operator. The local nature of this quantity is demonstrated with an example of the Aharonov-Bohm effect, proving that this gauge-invariant vector potential can be interpreted as the only source of the Berry curvature in the magnetic field. This weak value decomposition approach will lead to the extraction of new measurable quantities from traditionally unobservable quantities.
