# Help understanding Dirac's argument for magnetic monopoles

I'm trying to understand Dirac's argument for monopoles in his 1931 paper$^1$, but for me it's still a tough read (undergrad physicist).

I can begin to summarize his argument as follows: Take a very small closed curve. Assuming that the wave function is continuous, then the change in phase around a small closed curve must be small, which implies that the phase difference between different wave functions cannot be multiples of $2\pi$.

In the exceptional case that the wave function vanishes, the points at which it vanishes form a nodal line.

...but after this point I get completely lost. To clarify, I'm trying to summarize his "nodal line" argument into a short, clear argument that a group of fellow undergrads can understand.

1. P.A.M. Dirac. Quantized singularities in the electromagnetic field. Proc. R. Soc. London Ser. A 133, pp. 60–72 (1931).
• This answer of mine may be of interest to you. Please also include more context into your question so that people not familiar with Dirac's paper can tell what you are talking about without reading it - what is the situation here? (e.g. explain the wavefunction of what you're looking at here, or why its phase changes at all, etc.) – ACuriousMind May 4 '17 at 14:02
• Dirac's quantization argument uses that the wavefunction is singlevalued. – Qmechanic May 4 '17 at 14:20