The Magic of Strings
Relying on the recommend of the Lubonator in a very laudatory review posted to his blog and Amazon, I bought David McMahon’s String Theory Demystified and started going through it.
Perhaps you are familiar with the following “derivation:”
1 = Sqrt (1)
= (-1)*(i^2)*Sqrt(1) where i is the imaginary = Sqrt(-1)
= - Sqrt(i^4 * 1)
= - Sqrt(1) since i^4 = 1
= - 1
Truly an impressive result – even more so when you notice that steps 2-5 are utterly superfluous.
I mention this because David McMahon, in his book “String Theory Demystified,” uses the exact same trick to deduce that x * Sqrt(- m^2 / x) = - m * Sqrt(-x), (I have simplified a bit - he has lots of subscripts and superscripts and manages to throw in both more steps and a couple of cancelling sign errors.) (Pages 27-28, and yes, it did take him most of two pages).
This is hardly an inconsequential aside. The procedure is intended to illustrate how the so-called Polyakov action can be shown to be equivalent to the Nambu-Goto action.
Needless to say, this has shaken my faith in the idea that I can learn anything much about string theory from McMahon.
Wolfgang - I'm relying on you to check my work!