Recent content by DuckAmuck

From the Born Approximation, you can relate the potential to the scattering amplitude. So it follows that a potential can be derived from the scattering amplitude from Delbruck scattering. I tried to solve this myself, and get a scattering amplitude with only angular dependence, no momentum...

Chapter 7 of Griffith's particle book

The sigma tensor composed of the commutator of gamma matrices is said to be able to represent any anti-symmetric tensor. \sigma_{\mu\nu} = i/2 [\gamma_\mu,\gamma_\nu] However, it is not clear how one can arrive at something like the electromagnetic tensor. F_{\mu\nu} = a \bar{\psi}...

Looking to calculate the amplitude and cross section of the process: electron + positron to photon + Z boson. Basically the annihilation resulting in Z + gamma rather than gamma +gamma. My question is mainly about how to deal with the polarization states with the Z boson, since there are 3 and...

Yes, of course they are acting on different spaces in most cases. Was trying to keep things very generalized in an attempt to "rescue" invariance, but I think that may be overkill. And, Psi is indeed a dirac spinor. My question still remains on what to do about T being non-unitary. As ##A_\mu...

You see in the literature that the vector potentials in a gauge covariant derivative transform like: A_\mu \rightarrow T A_\mu T^{-1} + i(\partial_\mu T) T^{-1} Where T is not necessarily unitary. (In the case that it is ##T^{-1} = T^\dagger##) My question is then if T is not unitary, how is...

You’re right. I am just trying to figure out *how* this could be zero at this point, as in what conditions. Otherwise I’m stumped.

ok i think i have solid reasoning here: Suppose ##C^{ij} = M^{ij} + N^{ij}## From symmetry and antisymmetry we have: ##\epsilon_{ijkl} C^{ij}C^{kl} = 0## Also if you foil the CC product in terms of M and N you get ##C^{ij}C^{kl} = M^{ij}M^{kl} + N^{ij}N^{kl} + M^{ij}N^{kl} + N^{ij}M^{kl}##...

ep_{ijkl} M^{ij} N^{kl} + ep_{ijkl}N^{ij} M^{kl} The second term can be rewritten with indices swapped ep_{klij} N^{kl}M^{ij} Shuffle indices around in epsilon ep{klij} = ep{ijkl} Therefore the expression becomes 2ep_{ijkl}M^{ij}N^{kl} Not zero. What is wrong here?

Okay so the Lagrangian behavior is straightforward then. What about the Lagrangian density? Where rho is the mass density of a particle cloud. $$ \mathcal{L} = -\rho(y) \sqrt{\dot{y}_\mu \dot{y}^\mu} - A_\mu J^\mu -\frac{1}{4} F_{\rho\sigma} F^{\rho\sigma}$$ $$ \frac{\partial...

The last paragraph is basically asking, how do I write the full Lagrangian of a massive charged particle in an electromagnetic field? From what you've said, I gathered that it would be written like: $$ L = -m\sqrt{\dot{y}_\mu \dot{y}^\mu} - q A_\mu (y) \dot{y}^\mu - \frac{1}{4} \int d^3 x...

How would you unify the two Lagrangians you see in electrodynamics? Namely the field Lagrangian: Lem = -1/4 Fμν Fμν - Aμ Jμ and the particle Lagrangian: Lp = -m/γ - q Aμ vμ The latter here gives you the Lorentz force equation. fμ = q Fμν vν It seems the terms - q Aμ vμ and - Aμ Jμ account for...

Amazing. Thank you.

For example, can you predict the permittivity and permeability of a substance if you know what the atomic composition is? Is it a stat mech problem?

Maybe I'm not explaining it right. I swear I have seen this done before. Here is the process: Start with this generic form: R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} \pm \Lambda g_{\mu\nu} = \frac{8 \pi G}{c^4} T_{\mu\nu} Take the trace to get: -R \pm 4\Lambda = \frac{8 \pi G}{c^4} T Take the...