Monopoles,duality, triality

The existence of magnetic charges could be a raison d'être not only for the quantization of electricity in units $\text{1}\text{3}\text{e}$ but also for the confinement of the quarks at the end of “observable”, “electric” Dirac strings (quarks have no magnetic charge in this scheme). We first review the Dirac quantization condition, using a “sum over histories” approach, and get a more general result: A string attached to the dyon (e₁, g₂) is observable by a dyon (e₂, g₂) unless (1?x) e₂g₁ ? xe₁g₂ = nh, where x is an arbitrary parameter which reflects an ambiguity in the action principle. The Dirac and Schwinger-Zwanziger quantization rules are special cases, with $\text{x = 0}\text{and}\text{1}\text{2}$, respectively. Then, we look for the values of x and of the magnetic charges to “explain” that (i) the electric charge is quantized in units $\text{1}\text{3}\text{e}$, (ii) the string attached to an electron is unobservable, (iii) the string attached to a quark is observable. We find a denumerable set of solutions. In most cases, the magnetic charges also are connected with observable strings.