Feynman Diagrams: Polarization question

In summary, the conversation is discussing the correct polarization vector for a photon in order to conserve angular momentum when coupling with other particles. The polarization vector is given by $$\epsilon^\mu = (0, 1, i, 0)$$ and this is related to circular polarization in the z-direction. The speaker also mentions that the absolute phase of the polarization vector does not matter and suggests reading up on Special Relativity and Quantum Mechanics before diving into Quantum Field Theory.
  • #1
Breo
177
0
Hello folks,

I've just started to read "An Introduction to Quantum Field Theory by Peskin and Schroeder" and at the end of 6th page I could read:


"... Since H_I should conserve angular momentum, the photon to which these particles couple must have the correct polarization vector to give it this same angular momentum: $$\epsilon^\mu = (0, 1, i, 0)$$ ..."

Why those components? I lack of knowledge about polarization and don't know were it comes and what it means.

Thank you in beforehand
 
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  • #2
i has a phase shift of pi/2 relative to 1. That is exactly the condition for a circular polarization in z-direction. I don't have the book, so I don't know the exact context where this is used.

You could also use (0,i,-1,0) or similar as the absolute phase does not matter.
 
  • #3
Oh, I get it. I was blind as I'm new with 4-vectors and not used to plarizations concepts.

Thank you.
 
  • #4
by new to 4-vectors what do you mean? Don't read any QFT book if you are new to 4-vectors, but try instead some Special Relativity... Roughly said QFT= SR+ QM, so you need both QM and SR understanding.
 

Related to Feynman Diagrams: Polarization question

1. What are Feynman diagrams and how are they used?

Feynman diagrams are a visual representation of mathematical equations used in particle physics to understand and calculate the interactions between subatomic particles. They are used to simplify complex calculations and provide a visual understanding of the underlying physics.

2. How do Feynman diagrams represent polarization?

Feynman diagrams use arrows to represent the polarization of particles, with horizontal arrows indicating particles moving forward in time and vertical arrows representing antiparticles moving backward in time. The direction of the arrow also indicates the spin direction of the particle.

3. Can Feynman diagrams be used to calculate the polarization of all particles?

Yes, Feynman diagrams can be used to calculate the polarization of all particles, including photons, electrons, and quarks. They can also be used to calculate the polarization of composite particles, such as protons and neutrons.

4. How do Feynman diagrams account for the uncertainty principle in polarization?

The uncertainty principle states that the position and momentum of a particle cannot be known simultaneously. Feynman diagrams account for this by using a "virtual particle" line to represent a particle that exists for a very short period of time, allowing for the uncertainty in its position and momentum.

5. Are there any limitations to using Feynman diagrams to study polarization?

While Feynman diagrams are a powerful tool for understanding polarization, they do have some limitations. They only provide a simplified representation of the actual interactions between particles, and higher-order diagrams can become very complex and difficult to interpret. Additionally, they do not provide a complete understanding of quantum mechanics and should be used in conjunction with other mathematical models.

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