Homework for PHYS411, Fall 2001

1)

Section 12.3.2 discusses the field transformation under a Lorentz boost by $v$ in the $x$ direction. Use Eqs. (12.113) and (12.118) to show that $\bar{F}^{\mu \nu} = \Lambda^\mu_\lambda \Lambda^\nu_\sigma F^{\lambda \sigma}$ gives the correct transformation rules given in Eq. (12.108).

2)

When $J^\mu$ is given by Eq. (12.123), show that Eq. (12.126) reproduces all of Maxwell's equations.

3)

Solve Problem 12.56.

4)

Show that Eq. (12.132) gives Eq. (12.130).

5)

Verify Eq. (12.136).