First Homework

1) The virtual photon exchanged in the $ep$ scattering diagram discussed in class is space-like. Explain what this means and give an example of a similar process involving a time-like virtual boson.

2) Show that the quantity: $d^3p/2E$ is relativistically invariant. Briefly discuss its physical meaning.

3) By using Dirac's Equation and its conjugate, demonstrate that the covariant flux density is: $j^\mu = \bar{\psi}\gamma^\mu \psi$.

4) Making use of the anticommutation relation of the gamma matrices show that: $Tr(\gamma^\mu\gamma^\nu) = 4 g^{\mu\nu}$.

5) Show that for an electron at Jlab energies ($E_e= 6 GeV$), its mass can be disregarded in writing the energy-momentum relation.