What is a gauge (for someone who has not studied gauge theory)?

Question

I am taking a Quantum Mechanics II course and we were studying the relativistic corrections to the hydrogen atoms in perturbation theory. I was looking at the assignment, and a question is as follows:

Consider the non-relativistic Hamiltonian for a charged particle $-e$, in presence of an external, constant and uniform magnetic field $$B=\hat{e}_3B_0$$ in the symmetrical gauge $A=0.5B \times r $

But I don't understand what a Gauge is in this context. If I wish to find the Hamiltonian, what information is that supposed to give me? Could you explain to me what a gauge is for someone who has not had gauge theory, or link me to some basic bibliography to learn it?

yes, i have taken a course in electromagnetism. Next semester I will take electromagnetic theory, so my understanding is relatively basic — Nick Heumann, Jun 08 '19 at 01:10
Possible duplicates: https://physics.stackexchange.com/q/146585/2451 and links therein. — Qmechanic, Jun 08 '19 at 03:20
There are many choices of $\vec A$ that lead to the same $\vec B$. Such choice is called a gauge. — my2cts, Jun 08 '19 at 05:51

score 1 · Answer 1 · answered Jun 08 '19 at 00:58

1

A Hamiltonian of a particle in electromagnetic field is typically expressed via the 4-potential of electromagnetic field, which is defined up to a gauge transformation. The gauge in your case fixes the 4-potential.

answered Jun 08 '19 at 00:58

akhmeteli

26,888
2
27
65

@my2cts : I do not disagree, but I don't quite see your point. This does not seem to be in contradiction with my answer. – akhmeteli Jun 08 '19 at 05:27
@my2cts: So why don't you post your comment as an answer? – akhmeteli Jun 08 '19 at 05:47

What is a gauge (for someone who has not studied gauge theory)?

1 Answers1