Observation about the Classical Electromagnetic Gauge Transformation and Its Quantum Correspondence

Using the Landau and symmetric gauges for the vector potential of a constant magnetic field and the quantum problem of a charged particle moving on a flat surface, we show the classical electromagnetic gauge transformation does not correspond to a one-dimensional unitary group transformation U(1) of the wave function for the quantum case. In addition, with the re-examination of the relation between the magnetic field B and its vector potential A, we found that, in order to have a consistent formulation of the dynamics of the charged particle with both expressions, we must have that B=∇×A if and only if B≠0.

用相关同调概念统一表述电磁位和规范变换的尝试

对由非闭外微分式表示的电磁量，运用相关同调的概念引入其电磁位和规范变换，使闭微分式、非闭微分式的电磁位以及规范变换均可以统一地由相关同调的概念给出。