We review the formulation of gauge fields in terms of the frame of reference as well as the space in which the frame is defined. We highlighted some recent applications of gauge physics in the momentum space — in the modern fields of the spin Hall effect, the magnon Hall, the optical Magnus and the graphene valley Hall. General procedures of gauge transformation which lead to the construction of the gauge curvature and the equations of motion (EOM) are outlined. Central to this review is our intention to illustrate the impact of gauge physics on the past and future development of many new research fields emerging out of condensed matter physics, particularly in quantum nanosciences and nanoelectronics.

中文翻译：

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量子纳米科学中的规范场物理学

我们根据参考框架以及定义框架的空间来审查规范场的公式。我们重点介绍了规范物理在动量空间中的一些最新应用——在自旋霍尔效应、磁振子霍尔、光学马格努斯和石墨烯谷霍尔的现代领域。概述了导致规范曲率和运动方程 (EOM) 构造的规范变换的一般程序。这篇综述的核心是我们打算说明规范物理对凝聚态物理中出现的许多新研究领域的过去和未来发展的影响，特别是在量子纳米科学和纳米电子学方面。