# Recent content by lbrits

1. ### 3-d harmonic oscillator and SU(3) - how to imagine it?

Thanks, François. That's insightful. In any case, it's easy to see where the SU(N) comes from, but not terribly illuminating. If you work in the holomorphic representation, then the Hamiltonian is H = a^\dagger a which clearly has an SU(N) symmetry. This is also a very elaborate way of...
2. ### What is a multiplet?

If you did some quantum mechanics, then you might recall that the angular momentum states group themselves into multiplets labeled by j. Same thing is going on, except that for groups other than SU(2), you get more labels.
3. ### EM Field strength and plane waves

Blegh. It's a helluva long road. Quickest thing to do is to fix a gauge like the Lorenz gauge, and then find out what the Hamiltonian is. The factor of -1/4 will give you a canonical Hamiltonian that is something like \int\!dx\, \left(\frac{1}{2} \mathbf{E}^2 + \frac{1}{2}|\boldsymbol\nabla...
4. ### Is Zeta regularization real?

The point is that you were never performing an infinite sum to begin with (the theory isn't defined to arbitrarily short wavelengths). If you had a theory defined to arbitrarily small wavelengths, then the actual expression would look like your sum at low orders, and look like something else at...
5. ### Perplexing commutator

I think you're better off using [A,BC] = [A,B]C + B[A,C] and then integration by parts. Also, it's a good time in your life to realize that a commutator behaves very much like a functional derivative (recall QM 101).
6. ### Electron Concentration

A neutral gold atom has 79 electrons and mass of 3.27x10^-25 kg. As a metal, gold has a density of 19300 kg/m^3. So there are 5.90x10^28 atoms and 4.66x10^30 electrons in a cubic meter of gold. This is the "first year" answer. Hope that helps.
7. ### Clebsch-Gordan Theorem?

My suspicion is yes, but it will be hard. Smells like something that you'd do with Young tableaux. Edit: I think the CG theorem involves both symmetric and antisymmetric tensors. Do you know how to prove the theorem in the usual way (highest weight procedure)?
8. ### Peculiar feature of a commutator, can anyone explain?

You can also ask what is the operator conjugate to the number operator of the harmonic oscillator. Supposedly this is how Dirac found the creation and annihilation operators (though I'm not sure). In any event, you might want to look at the Weyl representation of the canonical commutation relations.
9. ### Virtual Photons

Perhaps best to say that virtual photons are the ones that you don't detect. The distinction is more of a practical one since photons themselves are "mathematical concepts/entities when you do perturbative expansions in quantum field theory". Forgetting this leads to problems like IR divergences...
10. ### Spin connection vs. Christoffel connection

I have made notes from various sources on this subject if you're interested http://www.mathematics.thetangentbundle.net/wiki/Differential_geometry/spin_connection [Broken] http://www.physics.thetangentbundle.net/wiki/Gravitational_physics/fermions_in_curved_space [Broken] I had to study this...
11. ### What's the relation between SUSY Generators and Covariant Derivatives?

When Q acts on a the most general function on superspace (superfield) Y = \phi + \bar\theta \psi + \bar\theta\theta F then it interchanges \phi and \psi (I'm ignoring the auxiliary field now), which is a SUSY transformation if you build your action out of superfields. Since you want non-trivial...
12. ### Strong force measurements

You can measure it in Newtons, if you want. But that's not very useful. The proton's, mass-energy comes form the binding energy of the quarks (negative), plus the masses of the individual quarks (positive), plus their relativistic kinetic energy (positive). The last two quantities are hard to...
13. ### Feynman diagrams

Well, it's the other way around. Anyway, you normally specify the incoming momenta, and integrate over the outgoing momenta. The momentum dependence of the 4pt function shows up in it's Fourier transform as well as from the LSZ formalism
14. ### Feynman diagrams

The matrix elements represent different possible momenta for the two incident particles.
15. ### Feynman diagrams

I disagree. Diagrams at a certain order have meaning and correspond to something physical, but many diagrams contribute *at a given order in the perturbation series*, and singling out one of them and asking "what does this diagram represent" is not always a good question. For example, IR...