added some of the original references:
W. Ehrenberg, R. E. Siday, The Refractive Index in Electron Optics and the Principles of Dynamics, Proceedings of the Physical Society. Section B, 62 8 (1949) 1 [doi:10.1088/0370-1301/62/1/303]
Yakir Aharonov, David Bohm, Significance of Electromagnetic Potentials in the Quantum Theory, Phys. Rev. 115 (1959) 485 [doi:10.1103/PhysRev.115.485, pdf]
Tai Tsun Wu, Chen Ning Yang, Concept of nonintegrable phase factors and global formulation of gauge fields, Phys. Rev. D 12 (1975) 3845 [doi:10.1103/PhysRevD.12.3845]
at Aharonov-Bohm effect I have polished/expanded the Idea-section and little and then I wrote out in some detail the standard 1-form vector potential that one uses to describe the effect.
]]>