Different representations of spinors

In summary, the conversation involves a new member greeting the staff and asking for help with a paper they have been struggling with. They have two specific questions about the paper, one regarding the meaning of a mathematical symbol and the other about an equation. The answer to their question can be found in Reference 10 of the paper.
  • #1
i_hbar
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First, greetings from newbie to "staff"

Now, let's start:

Since some days I'm struggling a little bit with this paper: http://jmp.aip.org/resource/1/jmapaq/v5/i9/p1204_s1?isAuthorized=no , especially with two questions:

1) On page 1205, II, A (right column): What does [itex]\tilde v B \gamma_5 [/itex] mean? The gamma 5 matrix isn't the problem, but what is the B and the tilde?? For me the "transpose-conjugate" of a (Dirac-)spinor should be more simply like [itex]v^{\dagger}\gamma_0[/itex].

2) Some lines later one finds the "basic equation". Isn't the term [itex]c_{\mu \nu} \gamma^{\mu \nu}[/itex] there equal to zero?

Thanks in advance.
 
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  • #2
The searched answer(s) can be read in Ref. 10 of the paper.
-> Problem is solved.
 

FAQ: Different representations of spinors

1. What are spinors and why are they important in physics?

Spinors are mathematical objects that describe the intrinsic angular momentum, or "spin," of particles in quantum physics. They are important because they allow us to accurately describe and predict the behavior of particles, particularly in the realm of relativity and quantum mechanics.

2. How are spinors represented mathematically?

Spinors are typically represented using matrices or vectors in a mathematical space. In some cases, they can also be represented as tensors or as elements of a Clifford algebra.

3. What is the difference between a Dirac spinor and a Weyl spinor?

A Dirac spinor is a four-component object that describes the spin of a particle with mass, while a Weyl spinor is a two-component object that describes the spin of a massless particle. They have different mathematical properties and behave differently under transformations.

4. How do spinors transform under rotations and Lorentz boosts?

Spinors transform under rotations and Lorentz boosts in a way that is different from vectors and tensors. They are typically transformed using spinor representations of the rotation and Lorentz groups, which involve complex numbers and allow for the incorporation of spin in the transformation.

5. What are some applications of spinors in physics?

Spinors have many applications in physics, including in quantum mechanics, particle physics, and general relativity. They are used to describe the behavior of particles, such as electrons, and to understand the symmetries and properties of physical systems. They also play a crucial role in the Standard Model of particle physics.

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