  Exterior calculus is a powerful tool to search for solutions to the
electromagnetic field equations, whose strength can be better appreciated when
applied to work out non-trivial configurations. Here we show how to exploit
this machinery to obtain the electromagnetic TM and TE modes in hollow
cylindrical waveguides. The proper use of exterior calculus and Lorentz boosts
will straightforwardly lead to such solutions and the respective power
transmitted along the waveguide.
