## Wednesday, May 10, 2017

### relativistic waves

a free massless scalar field $\varphi$ is described by the Lagrange density $\mathcal{L} = \partial_\mu\varphi\partial^\mu\varphi$, leading to an equation of motion $\partial_\mu\partial^\mu\varphi=0$, which is solved by plane waves travelling at the speed of light $c$. can you explain in what way electromagnetic (or gravitational) waves differ from scalar waves in this respect? where do their wave properties and propagation come from?