It appears to me that many results in complex analysis "kind of" have meaning in physics, but I struggle to find a clear explanation.
- Cauchy's integration theorem. It's quite common in physics to have contour integrals equal to zero in a potential. However, those potentials are all real-valued function, and I struggle to find a "complex-valued" example.
- Liouville's theorem, or Picardy's little theorem. I remember someone telling me about their meaning in physics, but I cannot remember it now. Can anyone give me a clue?
I would really appreaciate physical interpretation of other theorems as well.
Are there any good books that includes such interpretation in physics?