Electromagnetism helicity quantization

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... 

In quantized theory, this is an operator in the fermion field algebra. Assuming mo = 0, the mean value (0 Af 0) vanishes in the reference vacuum state because all momenta and currents cancel out. In a single-electron state a) = al 0), a self-energy (more precisely, self-mass) is defined by Smc2 = a Mc2 a) = a / d3x y0(—eji)i/ a). Only helicity-breaking virtual transitions can contribute to this electromagnetic self-mass. 

Phonons are quantized vibrational waves, just as photons are quantized electromagnetic waves. In each case the energy of the quasi-particle is given by the famous Planck formula, E — hv, where v is the firequency of the light, in the case of the photon, or the frequency of the vibration, in the case of the phonon. Vibrational waves in a periodic one-dimensional lattice such as an ordered linear or helical polymer are periodic both in time and in space. Thus they possess both a frequency and a wave length, A. 

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