(4.2) The relativistic equations studied in Chapter 3 gen- erally predict the the corresponding particles have Land g factor equal to 2. We can explore this for particles of spin using the Dirac equation. (a) A field obeying the Dirac equation in the pres- ence of a background electromagnetic field also obeys the second-order equation (iy Du + m)(iy Dv m) = 0, (4.45) where Du = (Ou + ie Au). Simplify this equa- tion by using the identity yy = = {y, } + { [vv]. (4.46) and show that it reduces to the Klein-Gordon equation plus one extra term. 8 t + m)o(t, 2) = 0. (b) Simplify the new term by proving the identity [Du, Dv] = +ieFuv. (4.47) Using the explicit form of the y matrices, evaluate this term in a background magnetic field for which Fij = ijkBh and Foi = 0. V = (c) Act the resulting equation on the Dirac equa- tion solution (3.50). (3.2) = ($) - e Show that, to first order in B, the energy of the state is shifted by a term of the form of AE = - B. In the expression for , identify g = 2. -imt (3.50)