Srednicki 43.10

by Lapidus
Tags: 4310, srednicki
 P: 259 Trivial question... How exactly does the minus sign arise in eq. 43.10? The sentence below states because the functional derivative goes through one spinor, but I can't see how that works... book is online here http://www.physics.ucsb.edu/~mark/ms-qft-DRAFT.pdf equation 43.10 is on pdf page 273 thank you
 P: 179 i'll take a shot. let me argue by analogy, maybe making the rule plausible. suppose i have anticommuting numbers x,y,h. and i'm given the expression yx and i want to differentiate it with respect to x. lacking any better choice i form the difference quotient $$\frac{d}{dx}(yx) = \lim_{h \rightarrow 0} \frac{1}{h} ( y(x+h) - yx )$$ $$= \lim_{h \rightarrow 0} \frac{1}{h} yh$$ now because the numbers are anticommuting i can't just cancel h. i have to first swap yh or h^(-1) and y and then i can cancel. $$= \lim_{h \rightarrow 0}\left( -y \frac{1}{h} h \right)= -y$$
 P: 259 qbert, I thank you very much!

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