1. When quantum physics is made consistent with relativity (as first done by Dirac in 1927) a number of remarkable physical features of fermions turn...

1. When quantum physics is made consistent with relativity (as first done by Dirac in 1927) a number of remarkable physical features of fermions turn out to be automatically in- cluded by the requirement of covariance (that is, that the equation have the same form in all inertial frames). Which one of the properties of fermions listed below is NOT demanded by covariance?

1. The fermion must have an antiparticle that has the same physical properties but op- posite charge.

2. The potential energy in the equation becomes much more complicated because it must have at least one part that is spin- dependent.

3. The fermion mass cannot be constant, but must vary as the included potential energy varies.

4. The fermion must have a spin.

2. One surprising failure of the Dirac equation predictions for hydrogen was first studied by physicist Willis Lamb, and is called the "Lamb Shift." Lamb found that the 2P1/2

and 2S1/2 states in hydrogen are not degen- erate, but differ very slightly in energy. An explanation of this small energy splitting was one of the great triumphs of Quantum Elec- trodynamics in the mid-20th Century. What physical feature explains this discrepancy? 

1. Interaction between the proton spin and the electron spin must be taken into ac- count.

2. The total angular momentum operator for the electron does not provide a good quantum number.

3. No one has ever been able to figure this out.

4. The electron and positron states mix to- gether and interfere,

5. Electrons in an atom appear to have slightly different mass than electrons in free space.

6. The Coulomb field itself must be quan- tized.