Magnetic helicity electromagnetic topology

Helicity is defined as a qualitative measurement of how a topological configuration is linked, knotted, or twisted. If A is the vector potential of electromagnetism, the quantity then defines magnetic helicity. In order to obtain a nonnull value for K, the condition A (V A) /- 0 must be verified in the volume... 

A very important property is that the magnetic and electric lines of an electromagnetic knot are the level curves of the scalar fields 4>(r, t) and 0(r, f), respectively. Another is that the magnetic and the electric helicities are topological constants of the motion, equal to the common Hopf index of the corresponding pair of dual maps constant with dimensions of action times velocity. 

As was shown in Section II, the magnetic and the electric helicities of any radiation electromagnetic field are equal. Moreover, in the case of the topological model, the helicities of the knots verily... 

In the previous section, it was shown that the constant a must be equal to [hc in order to obtain the right quantization of the electromagnetic helicity. This implies that the topological model predicts that the fundamental charge, either electric or magnetic, has the value... 

One of these topological constants of the motion is the electromagnetic helicity, defined as the semisum of the magnetic and electric helicities, which is equal to the linking number of the force lines... 

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