For example, the magnetic field B can be expressed in terms of the rotational of a vector potential, as is stablihed by Helmholtz Theorem, but this vector potential has any physical meaning like scalar potentials?
Physicists try hard to ensure that it does not have any meaning. This is called gauge invariance. Yet, there is Aharonov-Bohm effect where A is not zero, B is zero, yet wave function feels it. You
Edgar,
Besides subscribing to Igor's answer, I suggest you to see the form of the Hamiltonian for a particle in an electromagnetic field (https://en.wikipedia.org/wiki/Relativistic_quantum_mechanics#Spin-0) .
You can see there that the vector potential appears in the Hamiltonian, i.e. the particle energy depends on it. So, yes, this vector has physical meaning.
Nowadays the vector potential has several complementary meanings. Let me try to summarize the fundamentals.
The vector potential is the linear momentum per unit of charge. Therefore it is directly related with the Poynting vector for the fields and infinitesimally can be represented with translations generators . On the other hand it can be equated with the magnetic induction B by means of its curl when no trivial topology of its associated differential manifold. This enable us to give it a geometrical meaning (affine connection) for describing the electronic motion under magnetic singularities as it happens in the Aharonov-Bohm effect or in the Berry phase defined between electrodynamics and quantum mechanics.
- Badges
- Science topic
- Similar topics
- Physical Sciences
- Electromagnetism