In a Hilbert-space whose dimensionality is either finite or countably infinite, we have the discrete resolution of identity
\sum_n |n\rangle \langle n| = 1
In many cases, for example to obtain the wavefunctions of the discrete states, one employs the continuous form of the resolution...
Thanks for your replies, I have not had time yet to look into this more. I still think it's an interesting question, but my original motivation for it has disappeared, since I realized that a contour integral around a delta-function singularity will give 0, by simply looking at the definition of...
Does the Dirac delta have a residue? It seems like it might, but I don't know how to attack it, since I really know very little about distributions. For example, the Dirac delta does not have a Laurent-expansion, so how would you define its residue?
Hi,
For single-electron atomic systems, the electron can be specified by four quantum numbers n, l, m_l, m_s (principal, orbital, z-orbital, z-spin). The orbital quantum numbers are well defined since the problem is spherically symmetric.
However, for many-electron systems, the spherical...
I think one should not take the virtual particles too literally. Terms that look like intermediate particles (propagators) show up in the perturbation expansion of the interaction between two interacting external particles. However, their energies are allowed to take any value, not just those...
The Feynman slash
\slashed{a}=\gamma^\mu a_\mu
maps a four-vector a to its Clifford algebra-representation. This is a linear combination of the gamma matrices with the components of a acting as expansion coefficients. What physical significance does this new object have?
The gamma...
What is meant by saying that the Goldstone-bosons are "eaten" by gauge bosons?
I've seen this statement all over, but can't find a good explanation of what this actually means. Anyone care to shed some light?
K^2:
What do you mean by "at a distance"?
Do I understand you correctly like this:
* Prior to any electron/positron annihilation, a positronium bound system forms.
* This formation releases radiation.
* After formation, annihilation occurs, and the particles are effectively at rest...
Yes, that's true, but there are higher-order diagrams contributing in which one or more photons are exchanged before annihilation. So theory can take into account the Coulomb interaction, but the question is whether the energy shows up in experiments.
Yes, but that doesn't really answer my question.
I mean, if the energy balance of a process is out of order, it seems to me that the physics community would be well aware of it, trying to find a solution. Since this debate obviously doesn't exist, I imagine that the person who told me is...
When an electron and a positron annihilate, they typically produce two gamma rays, each of energy mc^2 plus whatever kinetic energy available before annihilation. I was recently told that it is an experimental fact that the electrostatic energy between the electron and the positron does NOT...
Thank you humanino for that answer. I'll have to think about it for a while.
Of course, you're right about the momentum-position stuff! Got a little mixed up in the old head...
Are point-particles "real"?
I've heard a couple of times the claim that the electron (among other elementary particles) is point-like, having essentially no spatial extension.
In the framework of QFT (which forms the basis of the standard model and therefore our best current understanding of...
So, if I end up with something like
\int d^3p f(p) \delta(p^0-a^0)
where the argument in the delta is zero from energy conservation, you're saying that I should regard this as
\int d^3p f(a)
?
Hi!
The Dirac delta satisfies
\int dx f(x) \delta(x-a) = f(a)
But how about
\int d^3x f(x) \delta^{(4)}(x-a)
Here, x and a are four-momenta, and the integral is over the regular 3-dim momentum.
How does the delta behave here?
Hi!
I am currently taking a first course in QFT with Peskin & Schroeder's book. I've got stuck with the equation that relates the differential decay rate of a particle A at rest into a set of final particles with the invariant matrix element M of the process. M can be found from the Feynman...
Could you expand on how my argument shows this?
Also, I think the fact that the equivalence principle is only locally true doesn't mean that gravity cannot be seen as accelerated reference frames. The way I understand it is that in order to everywhere cancel the effect of gravity we need...
I started thinking about this when studying the equivalence principle. Basically all of GR comes from the assumption that (locally) gravity and an accelating reference frame is the same thing. Right? Hence there is no way to tell whether you're at rest in a (locally homogeneous) gravitational...
From what I understand, Einstein basically scrapped the concept of gravity being a force and instead said that energy (and thereby mass) and momentum causes spacetime to curve. Objects still travel on geodesics in spacetime (Newton's first law), but since it is curved, the geodesics near massive...
Ok, so suppose that the helicopter is instead placed upon a rigid body. The distances between molecules in the supporting body are slightly compressed and thereby act as a bunch of tiny springs (if we assume that intermolecular forces can be modeled as derived from a harmonic potential). The...