The 4x4 spin 1/2 representation in electron polarization in a magnetic field

We introduce a 4x4 spin representation for spin 1/2. There are two spin orientations for a given value of g$_+$ and two for g$_-$ which arise for two signs of spin. This theory produces factors which affect the product m*g* so that if these factors are not taken into account, much larger values of the electron mass than those of the electron mass in a band arise. This predicted phenomenon is in accord with the experimental data. Similarly we find that factors arise in cyclotron frequency which affect the magnetoresistance and hence the g values. Accordingly, large g values are measured in the experimental data. When our factors are taken into account, the g values compare well with band values. The g*=g$_{\pm}-\delta$ describes the shift due to many-body interactions.