15 questions linked to/from Complex integration by shifting the contour
884 views

### Divergent integrals in QFT

I am starting to learn about QFT and something that I noticed is that integrals who would diverge otherwise are assigned a value if we do it by contour integration using the residues theorem and the ...
1k views

### How to choose the Correct Green's Function?

In order to solve the Green’s function of the Helmholtz operator $$(\nabla^2+k^2)G(\vec r-\vec r’)=\delta^{(3)} (\vec r-\vec r’)$$ one can obtain four different Green’s functions corresponding to four ...
874 views

### Feynman's $i \epsilon$ prescription in loop expansion

I have some questions about the $i\epsilon$ factor in Feynman diagrams. First, what is the physical meaning of $i\epsilon$ in loop amplitudes. Second, how does it ensures unitarity? And third, Dyson ...
666 views

### Fluctuation-dissipation theorem in QFT

If I understand correctly, the fluctuation-dissipation theorem (fdt) in QFT technically arises because of $\pm i\epsilon$ - infinitesimally small summand in the denominator of spectral representation ...
665 views

481 views

### How uniquely determined is the impedance of an infinite-chain circuit?

A recent question asked how to find the impedance of an infinite chain of series-plus-parallel circuits. The standard trick is to split the chain after the first link, and treat the tail of the ...
171 views

### Use of negative frequency for the sake of simplifying mathematics?

How can we use the idea of negative frequency for the sake of simplifying mathematics if negative frequency does not exist (to my knowledge) in nature ? For example, when plotting the spectra of a ...
127 views

### Path integral calculations $e^{i\omega 0^+}$

When computing correlation functions using the path integral formulation, I often need to compute integrals such as $$\int_{-\infty}^\infty \frac{d\omega}{2\pi} \frac{1}{i\omega -\epsilon}$$ ...
### Non-equivalence between $\omega \to \omega \pm i\varepsilon$ and Cauchy principle value
I am looking to gain a more rigorous and deeper understanding as to how an $i\varepsilon$ prescription actually changes the end result of a divergent integral, specifically in regards to Green's ...