Foldy-Wouthuysen Transformation of Properties

Free-Particle Foldy-Wouthuysen Transformation of Properties 

Since all unitary decoupling transformations have necessarily to start with the free-particle Foldy-Wouthuysen transformation Uo, it is convenient to introduce the free-particle Foldy-Wouthuysen-transformed operator 

For block-diagonal operators X, i.e., X = X = 0, as it is the case for electric field gradients, for example, all expressions are simplified to a large extent. 

A formal analysis of the size of picture-change errors is, however, by no means simple. Although one could immediately try to write down (for electric 

---