Thanks, it makes much more sense now. However, I can't see why different \epsilon regularizations should give the same results.
There are certainly many different fast-decaying functions, with which we can multiply the integrand, integrate, and then take the limit \epsilon\rightarrow 0 ...
Yes, but only for large enough imaginary part of p . There are non-vanishing contributions to the semicircle integral from the regions just above the real axis.
For the Jordan's lemma to be applicable, the integrand must have the form
f(p)e^{irp}
where |f(z)|\rightarrow 0 as |z|\rightarrow...
Not quite. This is clear from the fact that my expression is not well-defined, whereas theirs is well-defined. The discrepancy appears during the shifting as follows: P&S first write the original integral as (just manipulation of complex exponential)
D(x-y) = \frac{1}{8i\pi^2r}...
Hi, I've had the following problem in elementary quantum field theory. The propagator for the Klein-Gordon scalar field takes the form
D(x-y)=\int\frac{\textrm{d}^3\mathbf{p}}{(2\pi)^3}\frac{1}{2\sqrt{|\mathbf{p}|^2+m^2}}e^{-ip\cdot(x-y)}
I was interested what the propagator looks like for...
There is no principal difference between energy in classical and quantum physics. It is just a useful concept which helps physicists to calculate outcomes of experiments. Practically, however, it looks quite different in the 2 cases.
Classically, the energy of a system is defined as the...
I don't think the plates have to be conducting. They just have to respond to the electromagnetic field. In general, the Casimir, or Casimir-Polder forces are those that arise between objects through the exchange of virtual photons, so for example between an atom and a dielectric surface.
The...