A Potential between Photons via Delbruck Scattering

  • A
  • Thread starter Thread starter DuckAmuck
  • Start date Start date
  • Tags Tags
    Scattering
DuckAmuck
Messages
238
Reaction score
40
TL;DR Summary
Delbruck scattering generates potential between photons.
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 dependence. This seems to imply that the potential and force between two photons would be long-range? This is clearly incorrect. I would appreciate any help.
 
Physics news on Phys.org
It's hard to guess, what you did. Of course there's no "potential between photons". Delbrück scattering is described in leading order QED by box diagrams with four external photon lines. It's a pretty cumbersome calculation. See Landau&Lifshitz vol. 4.
 
  • Like
Likes topsquark and PeroK
On an unrelated note: Thank you! I didn't know the name for this. All I had heard of was "scattering of light by light."

-Dan
 
DuckAmuck said:
TL;DR Summary: Delbruck scattering generates potential between photons.

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 dependence. This seems to imply that the potential and force between two photons would be long-range? This is clearly incorrect. I would appreciate any help.
Perhaps worthwhile would be to post some if not all of your calculations. As a PDF would be ok.
 
First, I agree - we should call this "light by light" and not "Delvruck". It's closer to what you mean.

Next, at leading order, scattering is the same for attraction and repulsion. So the first order where it makes a difference is α6. I suspect that this is calculated somewhere, probably in someone's thesis. Maybe it's published somewhere.

Massless particles don't form bound states, so what is meant by attraction and repulsion needs to be carefully defined. Without doing the calculation (well beyond my abilities) I suspect there is a dependence on the relative phases of the photons.
 
The leading order are box diagrams with four vertices, i.e., the cross section is of order ##\alpha^4##. It's a genuinely relativistic effect of course, because it involves the massless photons, and thus you cannot expect that this has anything to do with potentials. It's also a pure quantum effect, i.e., due to quantum fluctuations of the quantum fields involved. As I said, you find the calculation in Landau and Lifshitz vol. IV. The calculation is indeed very cumbersome.

What's important to note is that this four-photon diagram is superficially logarithmically divergent. If it were really divergent, it would be a desaster for the renormalizability of QED, because there is no renormalizable counter term for such a divergence. Fortunately, gauge invariance comes to the rescue, and the Ward-Takashi identities tell you before you have done any calculation that indeed the four-photon vertex is finite. This is not true for any single box diagram but for the sum of all the 6 box diagrams.
 
  • Like
Likes strangerep and dextercioby
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I asked a question related to a table levitating but I am going to try to be specific about my question after one of the forum mentors stated I should make my question more specific (although I'm still not sure why one couldn't have asked if a table levitating is possible according to physics). Specifically, I am interested in knowing how much justification we have for an extreme low probability thermal fluctuation that results in a "miraculous" event compared to, say, a dice roll. Does a...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
Back
Top