Classical velocity and zitterbewegung

The result about the velocity obtained above is not what we expect from classical relativistic kinematics. In classical mechanics, the connection between the kinietic energy E, the momentum p, and the velocity v can be described by the formula 

In Dirac s theory the classical expression for E is replaced by the Dirac operator Hq. Translating the classical expression for the velocity into quantum mechanics would thus lead to the operator 

The inverse of the free Dirac operator can be explained as follows  

In momentum space, Hq is just the multiplication with the p-dependent matrix h(p) and the j-the component of the classical velocity is c pjh(p) . The 

Let us define the operator which describes the difference between the Dirac velocity ca and the classical velocity  

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