Transformation matrix from Dirac to Weyl

In summary, the conversation discusses the construction of a transformation matrix, S, that converts Dirac representations of gamma matrices into Chiral ones. The matrix must be hermitian and unitary, and the equation for S involves known matrices on both sides. The suggestion is made to write out ##\gamma_D^5## in the last equation as a starting point.
  • #1
Akineton
1
0
Hello friends, I'm trying to construct transformation matrix S such that it transforms Dirac representations of gamma matrices into Chiral ones. I know that this S should be hermitian and unitary and from this I arrived an equation with 2 matrices on the LHS (a known matrix multiplied by S from left) and another couple on the RHS (a known matrix multiplied by S from right). In addition, I have same equation with other known matrices. How can I find S from these?

The original question is attached.

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  • #2
You should post this in the home-work section of these forums! Hint: write out ##\gamma_D^5## in the last equation should be a good starting point.
 

Related to Transformation matrix from Dirac to Weyl

1. What is a transformation matrix from Dirac to Weyl?

A transformation matrix from Dirac to Weyl is a mathematical tool used in quantum mechanics to convert a Dirac spinor, which describes a particle with mass, into a Weyl spinor, which describes a massless particle. This transformation is important in understanding the behavior of particles in high energy physics.

2. Why is the transformation from Dirac to Weyl necessary?

The transformation from Dirac to Weyl is necessary because it allows us to study the behavior of massless particles, such as photons and neutrinos, which cannot be described by a Dirac spinor. It also simplifies the mathematical calculations involved in certain quantum mechanical equations.

3. How is a transformation matrix from Dirac to Weyl calculated?

The transformation matrix from Dirac to Weyl is calculated by using the properties of spinors and the Lorentz transformation. It involves converting the four-component Dirac spinor into two two-component Weyl spinors, and then using the appropriate matrices to make the conversion.

4. What are some applications of the transformation matrix from Dirac to Weyl?

The transformation matrix from Dirac to Weyl is used in various areas of high energy physics, such as particle accelerators and cosmology, to study the behavior of massless particles. It is also used in the study of neutrino oscillations and in the development of new theoretical models for particle interactions.

5. Are there any limitations to the transformation from Dirac to Weyl?

One limitation of the transformation from Dirac to Weyl is that it only applies to massless particles. It also does not take into account the effects of gravity, so it cannot be used to describe particles in a gravitational field. Additionally, the transformation only works for particles with spin 1/2 and does not apply to particles with higher spins.

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