The Foldy Wouthuysen and Dirac representations for a free particle

In due course we shall expand the Hamiltonian (3.101) still further by replacing 7r by (P +e A) and proceed to examine the magnetic vector potential and scalar electric potential in detail. 

The Foldy-Wouthuysen and Dirac representations for a free particle 

One can gain some insight into the nature of the Dirac wave equation and the spin angular momentum of the electron by considering the Foldy Wouthuysen transformation for a free particle. In the absence of electric and magnetic interactions, the Dirac Hamiltonian is 

In field-free, four-dimensional space, the sequence of Foldy-Wouthuysen transformations can be summed to infinity and written in closed form, 

The / is a function of (P/mc), to be chosen later, which will remove odd operators from the transformed Hamiltonian, and P = (P2)XI2. Now since S is not explicitly time-dependent, the transformed Hamiltonian is given from equation (3.66) by 

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