intrinsic angular momentum. Both correspond to Lorentz transformations, but in different ways. The presentation here follows that of Itzykson and Zuber. It is very nearly identical to that of Bjorken and Drell. A similar derivation in a general relativistic setting can be found in Weinberg. Here we fix our spacetime to be flat, that is, our spacetime is Minkowski space. Under a Lorentz transformation the Dirac spinor to transform as It can be shown that an explicit expression for is given by where parameterizes the Lorentz transformation, and are the six 4×4 matrices satisfying: This matrix can be interpreted as the intrinsic angular momentum of the Dirac field. That it deserves this interpretation arises by contrasting it to the generator of Lorentz transformations, having the form This can be interpreted as the total angular momentum. It acts on the spinor field as Note the above does not have a prime on it: the above is obtained by transforming obtaining the change to and then returning to the original coordinate system . The geometrical interpretation of the above is that the frame field is affine, having no preferred origin. The generator generates the symmetries of this space: it provides a relabelling of a fixed point The generator generates a movement from one point in the fiber to another: a movement from with both and still corresponding to the same spacetime point These perhaps obtuse remarks can be elucidated with explicit algebra. Let be a Lorentz transformation. The Dirac equation is If the Dirac equation is to be covariant, then it should have exactly the same form in all Lorentz frames: The two spinors and should both describe the same physical field, and so should be related by a transformation that does not change any physical observables (charge, current, mass, etc.) The transformation should encode only the change of coordinate frame. It can be shown that such a transformation is a 4×4 unitary matrix. Thus, one may presume that the relation between the two frames can be written as Inserting this into the transformed equation, the result is The coordinates related by Lorentz transformation satisfy: The original Dirac equation is then regained if An explicit expression for (equal to the expression given above) can be obtained by considering a Lorentz transformation of infinitesimal rotation near the identity transfomation: where is the metric tensor : and is symmetric while is antisymmetric. After plugging