4
votes
0answers
98 views

Complex integration by shifting the contour [migrated]

In section 12.11 of Jackson's Classical Electrodynamics, he evaluates an integral involved in the Green function solution to the 4-potential wave equation. Here it is: $\int_{-\infty}^\infty dk_0 ...
4
votes
1answer
138 views

Soft Bremsstrahlung: why $\hat{k}\cdot\mathbf{v}= \mathbf{v}'\cdot\mathbf{v}$?

On page 181 in Peskin & Schroeder they say that we consider the integral (intensity) $$\tag{1}\mathcal{I}(\mathbf{v},\mathbf{v}') = ...
2
votes
1answer
86 views

Angular momenta of photon

$A^\mu$ can have multipole expansions in classical electrodynamics. This gives rise to dipole photon, quadrupole photon etc. For dipole photon $j=1$ (In electrodynamics books they write it as $l=1$). ...
1
vote
0answers
68 views

Time derivative to energy equates $0$

Following up on a related question. This implies that, From the reference we can write \begin{align*} E(\lambda) &= I_F [g_\lambda ] + I_K [f_\lambda , g_\lambda ] + I_V [f_\lambda ] \\ & ...
5
votes
0answers
187 views

Semiclassical QED and long-range interaction

I'm interested in the (very) low energy limit of quantum electrodynamics. I've seen that taking this limit does not yield Maxwell equations, but a quantum corrected non-linear version of them. If ...
11
votes
1answer
531 views

Boundary conditions / uniqueness of the propagators / Green's functions

My question(s) concern the interpretation and uniqueness of the propagators / Green's functions for both classical and quantum fields. It is well known that the Green's function for the Laplace ...