Casimir trick for neutrinos

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In summary, the conversation discusses the application of Casimir's trick in electron neutrino scattering and the inclusion of nonphysical right-handed helicity states in the sum. The interaction vertex contains a projection onto the left-handed states, and in a world where only right-handed states interact, the vertex would change to ##\gamma^\mu (1+\gamma^5)##. The conversation also mentions the need for better explanation of missing logic links in the book.
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cipi
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Hello

I was reading in Griffiths that in the case of electron neutrino scattering, one can apply Casimir's trick to sum over input and output spin states, including the neutrinos. My question is, how come you are allowed to include in the sum the nonphysical right handed helicity state ? And, yes, I understand that the final average takes into account that there is only one neutrino spin. But how does the nonphysical helicity not contribute mathematically, since it is included ?

Thank you.
 
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The interaction vertex contains a projection onto the left-handed states.
 
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Orodruin said:
The interaction vertex contains a projection onto the left-handed states.
Thank you for answering, but trying to understand your answer, given that the vertex is γμ (1-γ5), in a world where only right handed states interacted, what would the vertex change to ?
 
  • #4
cipi said:
Thank you for answering, but trying to understand your answer, given that the vertex is γμ (1-γ5), in a world where only right handed states interacted, what would the vertex change to ?
##\gamma^\mu (1+\gamma^5)##
 
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  • #5
Orodruin said:
##\gamma^\mu (1+\gamma^5)##
Great, I wished missing logic links like this were better explained in the book for leisure readers like myself. Thanks.

I noticed 15 pages later that the book sort of explains it.
 
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1. What is the Casimir trick for neutrinos?

The Casimir trick for neutrinos is a proposed method for manipulating neutrinos using the Casimir effect, which is the attraction between two objects in a vacuum due to quantum fluctuations.

2. How does the Casimir trick work for neutrinos?

The Casimir trick for neutrinos involves placing two parallel plates in a vacuum and creating a difference in the energy density between the space above and below the plates. This difference in energy density would cause a net force on any neutrinos passing through the space, allowing for potential manipulation of their behavior.

3. What applications could the Casimir trick have for neutrinos?

The Casimir trick for neutrinos could potentially have applications in particle physics experiments, allowing for precise control and manipulation of neutrinos to study their properties. It could also have potential applications in technologies such as neutrino-based communication or energy production.

4. Is the Casimir trick for neutrinos currently being tested or implemented?

At this time, the Casimir trick for neutrinos is still a theoretical concept and has not been tested or implemented in any experiments. Further research and development is needed to determine its feasibility and potential applications.

5. What are some potential challenges or limitations of the Casimir trick for neutrinos?

One potential challenge for the Casimir trick for neutrinos is the difficulty in creating and maintaining a stable vacuum environment for the plates and neutrinos to interact. There may also be technical challenges in creating a significant difference in energy density between the plates. Additionally, the effects of the Casimir trick on neutrinos may be difficult to detect and measure accurately.

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