Classical limit from steepest descent

[jhaber]

I'm trying Zee's quantum field theory text as self-study (I'm years out of college) and about 100 pages into it. I can usually get something on the second or third reading. Oddly, one thing that keeps resisting me is quite early. In I.2, he says to apply an appendix on the method of steepest descent (Eq. 28) to get the classical limit of the path-integral formulation. I can follow the appendix but not its application. I believe I'm hung up on what happened to the factor, a square root, containing f'' in the denominator.

Thanks. A lot goes by quickly, with calculations left to the reader, and I'll try to keep questions to a bare minimum and, as here, as a last resort after a couple of weeks. Just the other day, say, it took me a bit to realize in II.1 what a spinor was, since it wasn't explicitly stated and to follow the transitions on p. 94, which began with a squared matrix producing a number (1) before formally shifting to its being a matrix giving the unit matrix. But I'm slowly getting things.

 

[NanakiXIII]

I don't see where that factor has gotten to either. Perhaps he simply neglected writing it down, since it doesn't really matter to the point he wants to make.

 

[jhaber]

Ah, thanks. Good way of looking at it. As long as Lagrange's equation comes out of it, we win.