Why does Dirac Equation describe spin 1/2 particles?

In summary, the conversation is about the confusion over why the Dirac Equation only describes spin 1/2 particles and not others. The answer lies in the 4x4 dimensionality of the alpha/beta/gamma matrices and the relationship to angular momentum. The book "Lectures on Quantum Field Theory" by Ashok Das and the article "Generalized total Angular Momentum Operator for the Dirac Equation in curved Spaced Time" by B. Carter in Physical Review provide further insight on the topic.
  • #1
bigbigtheory
2
0
Hi, Everybody!

Currently, I am reading the book "Lectures on Quantum Field Theory" (by Ashok Das)

But I am a bit confusing. Why does Dirac Equation describe spin 1/2 particles?
I have already known that Dirac Equation bears some angular momentum structure, but why it just describe spin 1/2 not others?

Thanks for answering.

Best wishes.
 
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  • #2
Please see: "Generalized total Angular Momentum Operator for the Dirac Equation in curved Spaced Time" by B. Carter in Physical Review, Vol. 19, No. 4, p. 1093-1097. The 1/2 spin relates to Dirac's eigenstructures. Feynman has a diagram about it you may find interesting.
 
  • #3
It's one of the wonders and puzzles of theoretical physics the fact that linearizing the K-G equation which properly describes spin 0 particles leads to an equation which describes spin 1/2 particles.

The answer to your "why" is simply <study the whole Dirac's argument>. Spin 1/2 follows naturally from angular momentum considerations, once the 4x4 dimensionality of the alpha/beta/gamma matrices has been proven.
 
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Related to Why does Dirac Equation describe spin 1/2 particles?

1. Why is the Dirac Equation important in understanding spin 1/2 particles?

The Dirac Equation is important because it accurately describes the behavior of spin 1/2 particles, which are fundamental building blocks of matter. This equation provides a mathematical framework for understanding the properties and interactions of these particles, and has been validated through numerous experiments.

2. What is the significance of the spin 1/2 value in the Dirac Equation?

The spin 1/2 value in the Dirac Equation refers to the intrinsic angular momentum of spin 1/2 particles. This value is a fundamental property of these particles and is responsible for many of their unique characteristics, such as their magnetic moment and their ability to exhibit spin-charge coupling.

3. How does the Dirac Equation explain the spin-statistics theorem?

The Dirac Equation provides a mathematical explanation for the spin-statistics theorem, which states that particles with half-integer spin (such as spin 1/2 particles) must follow Fermi-Dirac statistics, while particles with integer spin must follow Bose-Einstein statistics. This theorem is crucial for understanding the behavior of particles in quantum mechanics.

4. Can the Dirac Equation be applied to other types of particles?

While the Dirac Equation was originally developed for spin 1/2 particles like electrons, it has also been successfully applied to other types of particles, such as quarks and neutrinos. This equation has proven to be a powerful tool for understanding the behavior of various particles in the subatomic world.

5. How does the Dirac Equation account for the existence of antiparticles?

The Dirac Equation predicts the existence of antiparticles, which have the same mass as their corresponding particles but opposite charge. This is due to the fact that the equation has solutions for both positive and negative energy states, leading to the prediction of particles and antiparticles with opposite energy. This has been confirmed through experiments, such as the discovery of the positron (the antiparticle of the electron) in the 1930s.

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