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-dove
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I'm starting to read up a bit on QFT, starting with Griffith's intro to elementary particles book. I've gone through the background stuff and I'm now into the QED chapter. I was trying to get a feel for how the number of loops introduces free momentum variables, and I ended up drawing a diagram that got me wondering about photon decay (time flows from left to right for the sake of this post):
[PLAIN]http://img832.imageshack.us/img832/613/12photondecay.png
I couldn't figure out any reason for it to be kinematically forbidden (provided the decayed photons were collinear in the same direction as the original photon), yet I also couldn't find any literature on photon decay. After MUCH searching I found https://www.physicsforums.com/showthread.php?t=512811 which suggested that that diagram was forbidden by conservation of C-parity (since photons have -1 C-parity).
-So I guess my first question is, is this reasoning correct and does it prove that QED does not allow for a single photon to decay into two photons?
-Next, do the Feynman rules for calculating amplitudes explicitly encode conservation of angular momentum and C-parity? I can see the explicit conservation of energy-momentum via the delta function for each vertex. I can't quite see angular momentum conservation right away, although I wouldn't be surprised to see it follow somehow from some coordinate transform on the 4-momentum or something. The C-parity conservation I have no clue.
The thread that I linked made it sound like all photon decays are forbidden. However, the cited paper was a little over my head. So can anyone explain why the following diagram is not allowed?
[PLAIN]http://img853.imageshack.us/img853/9843/13photondecay.png
Three photons can combine to form spin 1, and the C-parity checks out fine.
-In light of the previous questions, if you actually try to do the integrals for these two diagrams do the amplitudes actually go to 0? i.e. do the Feynman rules explicitly forbid these interactions? This would surprise me just a tad (in the second case) considering that the following diagram is allowed:
[PLAIN]http://img26.imageshack.us/img26/9198/photonscattering.png
although clearly conservation of angular momentum checks out in that case.
-Now, even with all the above considered, can an even number of photons decay into a larger even number of photons? And likewise can an odd number of photons (greater than 1) decay into a larger odd number of photons? Or vice versa, can even/odd numbers of photons "combine" into less even/odd number of photons? Neither of these would cause an issue with the C-parity nor angular momentum. An example would be:
[PLAIN]http://img828.imageshack.us/img828/2918/24photondecay.png
(Sorry for the large images...I didn't realize it until previewing, and I don't feel like redrawing them all and reuploading them. I'll resize them next time.)
[PLAIN]http://img832.imageshack.us/img832/613/12photondecay.png
I couldn't figure out any reason for it to be kinematically forbidden (provided the decayed photons were collinear in the same direction as the original photon), yet I also couldn't find any literature on photon decay. After MUCH searching I found https://www.physicsforums.com/showthread.php?t=512811 which suggested that that diagram was forbidden by conservation of C-parity (since photons have -1 C-parity).
-So I guess my first question is, is this reasoning correct and does it prove that QED does not allow for a single photon to decay into two photons?
-Next, do the Feynman rules for calculating amplitudes explicitly encode conservation of angular momentum and C-parity? I can see the explicit conservation of energy-momentum via the delta function for each vertex. I can't quite see angular momentum conservation right away, although I wouldn't be surprised to see it follow somehow from some coordinate transform on the 4-momentum or something. The C-parity conservation I have no clue.
The thread that I linked made it sound like all photon decays are forbidden. However, the cited paper was a little over my head. So can anyone explain why the following diagram is not allowed?
[PLAIN]http://img853.imageshack.us/img853/9843/13photondecay.png
Three photons can combine to form spin 1, and the C-parity checks out fine.
-In light of the previous questions, if you actually try to do the integrals for these two diagrams do the amplitudes actually go to 0? i.e. do the Feynman rules explicitly forbid these interactions? This would surprise me just a tad (in the second case) considering that the following diagram is allowed:
[PLAIN]http://img26.imageshack.us/img26/9198/photonscattering.png
although clearly conservation of angular momentum checks out in that case.
-Now, even with all the above considered, can an even number of photons decay into a larger even number of photons? And likewise can an odd number of photons (greater than 1) decay into a larger odd number of photons? Or vice versa, can even/odd numbers of photons "combine" into less even/odd number of photons? Neither of these would cause an issue with the C-parity nor angular momentum. An example would be:
[PLAIN]http://img828.imageshack.us/img828/2918/24photondecay.png
(Sorry for the large images...I didn't realize it until previewing, and I don't feel like redrawing them all and reuploading them. I'll resize them next time.)
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