2016/06/18 by Bertrand Berche, D. Malterre, Daniel Malterre +1
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Gauge boson #Gauge fixing #Gauge theory #Introduction to gauge theory #Mathematical physics #Observable #Physics #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum mechanics #Supersymmetric gauge theory #Theoretical physics #quant-ph
paper · pdf · doi:10.1119/1.4955153
published as Am. J. Phys. 84 (2016) 616-625
arxiv created 2016/06/18 · openalex publication_date 2016/07/20 · openalex created_date 2016/07/22 · arxiv updated 2017/11/03 · openalex updated_date 2026/08/05
We are taught that gauge transformations in classical and quantum mechanics do not change the physics of the problem. Nevertheless, here we discuss three broad scenarios where under gauge transformations: (i) conservation laws are not preserved in the usual manner; (ii) non-gauge-invariant quantities can be associated with physical observables; and (iii) there are changes in the physical boundary conditions of the wave function that render it non-single-valued. We give worked examples that illustrate these points, in contrast to general opinions from classic texts. We also give a historical perspective on the development of Abelian gauge theory in relation to our particular points. Our aim is to provide a discussion of these issues at the graduate level.