Heart Strings
There is a famous Sidney Harris cartoon where a character has covered a blackboard with equations, in the midst of which he has written "and then a miracle happens" while a second character says "I think you need to be more explicit here in step two." It's a very funny cartoon, but the annoying pedant in me hates it when he encounters the equivalent in a textbook. One of my infamous examples occurs where a famous meteorologist was trying to derive a thermodynamic equation in his book on Dynamic Meteorology but the sign of a key factor turned out wrong. This happened because he didn't keep track of which state variables were held constant, but he apparently didn't realize it, so he invented some total BS reason to arbitrarily change the sign.
All this is prolog to declaring that my infatuation with Barton Zwiebach's A First Course in String Theory has hit a major snag. I really loved the first 11.5 chapters of this book. It's full of interesting and exciting stuff, exquisitely presented pedagogically, all carefully worked out so that a senior physics major (and even a slightly pre-senile PhD who has forgotten most of what little he once knew) can understand it.
Until, that is, we get to the calculation of the central extension of the Virasaro Algebra, which appears to be a major punch line of the book (extra dimensions, for example, seem to come from that). Around page 224 he starts getting a little sketchy about the algebra, and between equations 12.136 and 12.137 he rather arbitrarily discards two terms and then even more arbitrarily adds in two more (for example, changing
AD[B,C] to [A,D][B,C] where [a,b] is the commutator of a and b). This sent me into a deep funk until I managed to produce some algebra that convinced me that the discarded terms were equal to those introduced. So why didn't he say so?
Of course I now realize that anybody who actually understands this post will probably know enough to see how silly my concerns are. The hazards of posting after my regular bedtime!
All this is prolog to declaring that my infatuation with Barton Zwiebach's A First Course in String Theory has hit a major snag. I really loved the first 11.5 chapters of this book. It's full of interesting and exciting stuff, exquisitely presented pedagogically, all carefully worked out so that a senior physics major (and even a slightly pre-senile PhD who has forgotten most of what little he once knew) can understand it.
Until, that is, we get to the calculation of the central extension of the Virasaro Algebra, which appears to be a major punch line of the book (extra dimensions, for example, seem to come from that). Around page 224 he starts getting a little sketchy about the algebra, and between equations 12.136 and 12.137 he rather arbitrarily discards two terms and then even more arbitrarily adds in two more (for example, changing
AD[B,C] to [A,D][B,C] where [a,b] is the commutator of a and b). This sent me into a deep funk until I managed to produce some algebra that convinced me that the discarded terms were equal to those introduced. So why didn't he say so?
Of course I now realize that anybody who actually understands this post will probably know enough to see how silly my concerns are. The hazards of posting after my regular bedtime!
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