Spin and helicity

In direct analogy to the nonrelativistic theory of the spin, the self-adjoint matrix 

Here the symbol x means the vector product. Hence, for example, the third component of S is given by 

The plane waves obtained above are eigenvectors of the operator S p 

It is easy to determine the action of the helicity operator on the parts of a wave packet in the decomposition (53). 

Hence a wave packet which has a positive helicity at the intial time to has a positive helicity for all times. We want to stress that the spin itself is not a conserved quantity. 

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