Polarization of photon-Peskin and Schroeder

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SUMMARY

The discussion centers on the polarization of photons as described in the quantum field theory text "An Introduction to Quantum Field Theory" by Peskin and Schroeder. The user encounters confusion regarding the statement that the amplitude vanishes unless the final photon is right-handed, particularly when applying the polarization vector ε = (0,1,i,0). A key point raised is the difference in conventions for Jones vectors, where right-polarized is typically represented as (0,1,-i,0), which may impact the calculations. The user seeks clarification on the relationship between photon polarization and their calculations.

PREREQUISITES
  • Understanding of quantum field theory concepts
  • Familiarity with Peskin and Schroeder's "An Introduction to Quantum Field Theory"
  • Knowledge of photon polarization and its mathematical representation
  • Basic understanding of Jones vectors in optics
NEXT STEPS
  • Review the section on photon polarization in Peskin and Schroeder's text
  • Study the conventions of Jones vectors and their applications in quantum mechanics
  • Learn about the implications of right-handed and left-handed photon states
  • Explore additional resources on quantum field theory to clarify photon interactions
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Students and researchers in quantum field theory, physicists working with photon polarization, and anyone interested in the mathematical foundations of quantum mechanics.

ndcat10
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Hi, I am currently studying quantum field theory with worldwidely used text written by Peskin and Schroeder. On page 165 of that text it says, " the amplitude vanishes unless the final photon is right-handed." But I cannot figure out how it works. With ε = (0,1,i,0), I get same expression located right after 5.100, which result in 0 when it applies to u_R = \pmatrix{ 0 \cr 1}. I think there must be something related to photon polarization and I am missing. Could you find where I got wrong? Thanks in advance.
 
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I'm not sure if this is the issue you're having since I don't have my book in front of me, but I know they use a different convention than most on the Jones vectors. Usually, right polarized is (0,1,-i,0). Maybe this would make a difference?

http://en.wikipedia.org/wiki/Jones_vector#Jones_vectors
 
I still cannot figure out the connection between Jones vectors and my problem. Anyway thanks a lot :)
 

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