Recent content by weejee

I think you can view (3.1.13) as the definition of in/out states.

I think you need to look for how many disconnected pieces there are in the order parameter space.

\frac{1}{x+i\eta} = \frac{x}{x^{2}+\eta^{2}} - i\frac{\eta}{x^{2}+\eta^{2}} Can you convince yourself that \frac{\eta}{x^{2}+\eta^{2}} is pi times the delta function?

'P' means Cauchy principal value. http://en.wikipedia.org/wiki/Cauchy_principal_value

I'm now reading your paper on renormalization. It is quite illuminating and what you have said makes more sense now. It also seems far more efficient than asking you every single question at this forum. Anyway, thanks a lot!

Well, I was wondering if we can tell whether the bare theory is unphysical, simiply by looking at the field equation. Are you saying that it is the causality requirement which makes certain relativistic field theories unphysical at the bare level? As for field equations of interacting condensed...

I kind of see where my confusion comes from. In condensed matter, we just define the "bare" theory in the Fock space. (The contents in the bare theory are already renormalized in the high-energy sense, but if there is something like the Fermi sea, we can expect further renormalization of the...

That's right. Still, when we have a physical cutoff, can't we relax our view on the bare quantities that they are purely figurative, and think about some Hilbert space even at the bare level? Maybe the conclusion is dependent on what kind of cutoff we have?

According to your viewpoint, bare quantities and perturbative corrections to them are purely formal things, and they just give us some rules to obtain renormalized quantities? Is it that you don't even think about the Hilbert space before renormalization? I wonder. Maybe to have a UV complete...

Considering my condensed matter background, it doesn't sound natural to me to regard only the renormalized(or physical) quantities as real and consider bare quantities and the renormalization process as purely figurative or mathematical things. I believe that I allow virtual particles some more...

Do you have some background in quantum mechanics? There, people talk about "real" or "virtual" transitions between different energy levels. Being real or virtual in quantum field theory mean pretty much the same thing, although renormalization complicates the problem. Anyway, the example you...

I actually think that Schumm's line of argument can be quite misleading. Still, since I'm not sure how to explain it any better in terms of ordinary language, I'll just add things to his explanation. 1. As Schumm said, the frequency and also the momentum of the virtual photon divide themselves...

Could you elaborate a little bit? For example, Laurent expansion of which function around which point? Shouldn't we still have some (usually finite) region of convergence? Or are you saying that we don't need to associate X and Y with definite numbers and consider the formula as some formal...

I have been confused about this. For example, when we talk about mass/wavefunction renormalization, we use the following relation to extract the "self energy" from the perturbation expansion of the propagator. \frac{1}{X-Y} = \frac{1}{X} + \frac{1}{X}Y\frac{1}{X} +...

Afaik, the justification goes like this: Although the expression for the perturbative correction is formally infinite, it diverges only logarithmically (~\alpha \ln \frac{\Lambda}{m_{e}}), where \Lambda is the cutoff (some energy scale over which the theory isn't valid), and we know that the...