What it would look like if Wolfgang Amadeus Mozart decided to discuss A440, concert pitch (440 Hz), on 24 pages?

Today, you may see the answer to a very similar question. Edward Witten finally attempted to solve a homework problem given not only to him by his (former) doctoral adviser in 1989 and wrote

The Feynman \(i\varepsilon\) in String Theory.

Almost all particle physicists learn about the \(i\varepsilon\) prescription in their introductory courses. The Feynman propagators have to have the form\[

\frac{-i}{p^2+m^2-i\varepsilon}

\] in the mostly positive \(({-}{+}{+}\cdots{+}{+})\) signature that Witten prefers. The extra infinitesimal term tells us in what direction we should circumvent the singularity when we integrate over the momenta in the loops and that's why it matters. In the position basis, the addition of the infinitesimal imaginary term answers the question whether the propagators are retarded or advanced or something in between. Yes, C) is correct: they are Feynman propagators, stupid.

Note that the extra term adds an imaginary term to something that you could naively try to define by the real principal value because\[

\frac{1}{z-i\varepsilon} = {\rm v.p.} \frac{1}{z}+i\pi\delta(z).

\] I would always say that you may imagine that this \(i\varepsilon\) is an infinitesimal limit of something like \(i\Gamma/2\) coming from a finite width (decay rate) – even if the lifetime is infinite, it has to be there for the stable intermediate particle to behave just like the unstable ones. There can't be any discontinuity if you just send the lifetime to infinity and because the form of the propagator seems obvious for the unstable particles (whose wave functions exponentially decay with time), a "trace" of the exponential decrease with time has to be inserted to the stable particles' propagators, too. This is a moment in which the arrow of time enters the fundamental formulae, by the way.