Interesting, I have not heard of this convention to treat the vertices differently by complex conjugation. Do you have any references for this particular notion?
Also, I have not seen ##(k^2-m^2+i\epsilon)^{-1} \rightarrow 2 \pi \delta(k^2-m^2)## in any reference I have, for example...
OKay, so whenever I run into explanations on the cutting rules, most of the time I see the statement to replace##\frac{1}{p^2 - m^2 + i\epsilon} \rightarrow -2i\pi \delta(p^2 - m^2)## for each propagator that has been cut
taking note that there is no factor of i in the numerator for...
for a given diagram in some interacting theory that needs a momentum cutoff
shouldn't the same momentum cutoff be used for diagrams that don't need a momentum cutoff for convergence
for example, phi3 theory has a self energy diagram that diverges, so if one imposed a momentum cutoff there...
So I've seen this type of integral solved. Specifically, if we have
∫e-i(Ax2 + Bx)dx then apparently you can perform this integral in the same way you would a gaussian integral, completing the square etc. I noticed on wikipedia it says doing this is valid when "A" has a positive imaginary part...
Ultimately I am trying to understand it in the context of localized field configurations (let's say on a torus S1×S1) and the uncertainty associated with those field configurations.
Intuitively it seems there should be a maximum uncertainty on the localization of an event in this torus. The...
Well the strange thing to me is that, let's say we are given some field configuration with the appropriate periodicity in the compactified domain. When we Fourier transform this function, it will in general be nonzero over the entire domain.
But if in the field theory we are only interested in...
Integrating the lagrangian over spacetime in regular field theory (by regular i mean field theories with noncompact dimensions) gives the action. To do this, one integrates over all spacetime , minus infinity to plus infinity in each dimension. For field theories with compactified dimensions...
Is this possible? It seems like it should be but, it's difficult to find an explicit relationship between a general function of one variable x (let's say we are only interested in functions that decay to zero as they go to plus or minus infinity)
it seems like summing a bunch of gaussians of...
Can anyone point me to some material on applying the Fourier transform to the case of an analytic function of one complex variable?
I've tried to generalize it myself, but I want to see if I'm overlooking some important things. I've started by writing the analytic function with
u + iv where u...
More generally, the normal ordering produces a vanishing expectation value because either it annihilates the vacuum state sending it to zero, or it changes the bra or ket vector into a state that is orthogonal to the vacuum state (like in the first example) and so this also gives zero...
Well, there are a few possibilities for the normal ordered product. To convey the point it is enough to think of the normal ordered product of two creation/annihilation operators.
for the first example we have
ap†ap†
where ap† corresponds to the creation of a particle with momentum p.
now...
to my understanding, wick's theorem gives a way to represent the time ordered combination of field operators. it turns out, via wick's theorem that you can think of the time ordered product as a sum of normal ordered products and contractions.
since we are interested in the vacuum expectation...
is there a discussion somewhere on the notion of an advanced or retarded feynman propagator.
i don't mean the advanced or retarded propagator juxtaposed against the feynman propagator. I mean the feynman propagator itself with a theta step function multiplied by it to effectively give an...