Friday, 27 February 2015

quantum field theory - Fourier Transforms Related to Green's Functions


I'm reading a text on field theory where there are a number of assertions made about Fourier transforms that I'm finding confusing. For example, let GR=iθ(tt)eiω0(tt). The text says that the FT of GR wtih respect to tt is (ϵω0+i0)1. What is the meaning of this i0 term?



Secondly, after inverting this expression the text takes the inverse transform. That is, the inverse FT of ϵω0+i0 and obtains δ(tt)(itω0+i0). What is the meaning of this? How did the fourier transform of an expression become an operator?


Thanks!




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