Helicity fermions

The density is related to the total number of bosonic and fermionic helicities... 

The signs of spatial components are reversed in the corresponding contravariant 4-vectors, indicated by x etc. Dirac matrices are represented in a form appropriate to a 2-component fermion theory [38], in which helicity y5 is diagonal for zero-mass fermions,... 

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. 

We know from Section 1.3.1 that the fermions and antifermions must have opposite helicity, so only two decay amphtudes occur, M+ and M +. Moreover if in (5.1.3) we write... 

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