Recent content by welcomeblack

Hi all, Just doing some hobby physics while I put off working on my research. In one dimension, the function \begin{equation} f(a,b)=[1-\exp(-(a-b)^2)] \end{equation} vanishes when a=b. In Minkowski spacetime though, such a function is not so easy to find (if you require Lorentz invariance). If...

This thread's a bit old but I'd like to answer this question for people in the future. You're doing fixed-order perturbation theory at order ##\alpha##, which means you drop terms of order ##\alpha^2## You can recognize ##d\alpha / dln \mu## as the beta function, which starts at order...

Ohhh okay I get it. Thanks for your help!

I've seen something similar used in mean field theory to estimate the partition function of some difficult to calculate system. I think the particular step that reminds me of your equation is called the Bogoliubov Inequality.

Hi all, I'm working on some QFT and I've run into a stupid problem. I can't figure out why my two methods for evaluating i\gamma^\mu \partial_\mu \exp(-i p \cdot x) don't agree. I'm using the Minkowski metric g_{\mu\nu} = diag(+,-,-,-) and I'm using \partial_\mu =...

jkl71: The time t is just a coordinate on the manifold that every observer can agree on, but is not actually an observable. The proper time \tau is what the observer actually measures, and is different for each observer, so I labelled them with indices according to which observer the proper time...

Hi all. I'm taking a course in GR and trying to get my intuition and mathematical techniques up to speed. I've been trying to derive the velocity addition formula in Minkowski space, but for some reason I can't do it. Here's what I have: I'll use the Minkowski metric of signature...

Okay so the spinor components on the LHS are the same as those on the RHS. Avoiding any spinor division (since fzero says it isn't generally well defined), if we take the partial of (psibar*psi)(psibar*psi) with respect to psibar, we get from the LHS \frac{\partial}{\partial\bar{\psi}}...

Hi all, I've been playing around with spin 1/2 Lagrangians, and found the very interesting Fierz identities. In particular for the S x S product, (\bar{\chi}\psi)(\bar{\psi}\chi)=\frac{1}{4}(\bar{\chi} \chi)(\bar{\psi} \psi)+\frac{1}{4}(\bar{\chi}\gamma^{\mu}\chi)(\bar{\psi}\gamma_{\mu}...

I've been thinking about chapter 11 of Griffiths' Introduction to Elementary Particles. In section 11.7, he gives the Lagrangian density \mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)+\frac{1}{2}\mu^{2}\phi^{2}-\frac{1}{4}\lambda^{2}\phi^{4} and shows that the minimum...

For my explanation, you need to know some elementary QM. The probability to go from initial state to final state is the probability amplitude squared. This probability amplitude is denoted <f|i>, so P(i→f)=|<f|i>|2. The total probability amplitude is the sum of all indistinguishable paths...

Sweet. Thanks a bunch.

Every paper I read about cross-section measurements from colliders has a line saying (for example): ...positron-electron annihilations at \sqrt{s} = 40 GeV are studied... 1) What does this mean? I'm guessing it means that in the CM frame, the energy of each beam is 40 GeV. 2) Why use...