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(t−t′)e−iω0(t−t′). The text says that the FT of GR wtih respect to t−t′ is (ϵ−ω0+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 ϵ−ω0+i0 and obtains δ(t−t′)(i∂t′−ω0+i0). What is the meaning of this? How did the fourier transform of an expression become an operator?
Thanks!
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