Wednesday, December 23, 2009

Maxwell in higher dimensions

They said you couldn't teach string theory to undergraduates. They said that as string theory is a quantum theory of gravity, you had to learn general relativity first (as well as QFT). They said it was all too speculative anyway, a journey into a pointless cul-de-sac.

I'm most of the way through chapter 3 of "A first course in string theory" and in this chapter we've looked at the formulation of electromagnetism in two spatial dimensions (flatland) as well as its extension to spaces with an arbitrary number of spatial dimensions (≥ 2). This is enormously enlightening and really exposes the fundamental structure of the theory.

I finished today with a section entitled "Gravitation and the Planck length". Tomorrow, to end the chapter I'll be covering "Gravitational constants and compactification" and "Extra large dimensions". Seriously, I can hardly wait.

The approach is quite mathematical, with extensive use of raised and lowered indices and Einstein's summation notation. It would be accessible to a bright undergraduate who had mastered their modules on electromagnetism, quantum theory and special relativity.

Looking ahead, chapter 4 is entitled "Nonrelativistic strings" and focuses on string equations of motion and Lagrangian dynamics.