Recent content by DOTDO

In Peskin and Schroeder's QFT book, while deriving the cross section formula for particles ##A## and ##B##, a Dirac delta appears in Eq 4.77: \begin{align} \nonumber \int d\bar{k}^z_A \, \left. \delta ( F ( \bar{k}^z_A ) ) \right\vert_{\bar{k}^\perp_A = k^\perp_A, \, \bar{k}^\perp_B = k^\perp_B}...

S. Weinberg says in his book, "The Quantum Theory of Fields Volume I", that Since electrons carry a charge, we would not like to mix annihilation and creation operators, so we might try to write the field as $$\psi(x)=\sum_{k}u_k (x)e^{-i\omega_k t}a_k$$ where ##u_k (x)e^{-i\omega_k t}## are a...

Hi. I have thought that the variables q and q' in L = L(q, q') are independent. (q' = dq/dt) Of course q and q' are functions of time t , but they are only dependent in terms of t . However, in the sight of general(or abstract? I mean, not specific) functional L(q, q'), q and q' are just...

Hi I'm studying electron-muon scattering and now considering the Lorentz invariant integration measure. The textbook introduced it, which use dirac delta function to show that d3p/E is a Lorentz scalar. I understood it but I wanted to find other way and tried like this: I need a hint on the...

Hi I read that for Dirac equation, [ L , H ] =/ 0 , so Dirac found a operator S such that 1. [ S , H ] = - [L, H] ---> [ J, H ] = 0 where J = L + S , the total angular momentum. 2. S gives an eigenvalue of spin 1/2 ---> solutions of Dirac equation describe fermions. The total...

Hi I began to study the basics of QED. Now I am studying Lagrangian and Hamiltonian densities of Dirac Equation. I'll call them L density and H density for convenience :)Anyway, the derivation of the H density from L density using Legendre transformation confuses me :( I thought because...

If we consider E and B individually, there are 6 total degrees of freedom. But they are actually related to each other by Maxwell's equations. So we can find potentials and reduce dof to 4; 3 in vector potential and 1 in scalar potential. Thus, there remain 2 redundant dof. This is the...

Hi. In class, the professor has tried to derive the equation by using the principle of least-action. (But not yet completed. Maybe next class...) However I heard this method is used by Hilbert, who had derived the equation 5 days before Einstein derived it. Then, what method did Einstein use...