First Homework

1) Show that the quantity: d³p/2E is relativistically invariant.

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

(Section 5.2 of Halzen-Martin).

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

4) Show that for an electron at Jlab energies (E_e= 4 GeV), its mass can be disregarded in writng the energy-momentum relation.