How do one describe particles with chirality?

In summary, particles can be described with chirality using Weyl and Dirac equations, which are interchangeable. The term "electron" usually includes both left-handed and right-handed components, which can be extracted using projection operators. In solid state systems, electrons of different chirality can be found in the conduction and valence bands, with clockwise and anti-clockwise spins respectively. An example of interaction between particles with different chirality is the formation of excitons in the electron-hole interaction.
  • #1
iamquantized
28
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1) How do one describe particles with chirality? Dirac and Weyl equation?

2) Are particles of different chirality interacts?

3) Does electron have chirality?
 
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  • #2
1) Weyl spinors describe paricles with a definite chirality. Dirac spinors incorporate degrees of freedom for both chiralities. You can extract the desired chirality from dirac spinors with the projection operator [tex]P_\pm = 0.5 (1 \pm \gamma^5)[/tex]. As a result, both desciptions are fine and in fact interchangable.

2) Pls try reposting the question.

3) The term "electron" ususally means both, the left-handed and the right-handed electron. You can either treat it as two different Weyl fields (the left- and right-handed electron) or, as usually done, as a single Dirac spinor. In the latter case, you can still unambigiously project on its left- and right-handed components.
 
  • #3
Timo said:
1) Weyl spinors describe paricles with a definite chirality. Dirac spinors incorporate degrees of freedom for both chiralities. You can extract the desired chirality from dirac spinors with the projection operator [tex]P_\pm = 0.5 (1 \pm \gamma^5)[/tex]. As a result, both desciptions are fine and in fact interchangable.

2) Pls try reposting the question.

3) The term "electron" ususally means both, the left-handed and the right-handed electron. You can either treat it as two different Weyl fields (the left- and right-handed electron) or, as usually done, as a single Dirac spinor. In the latter case, you can still unambigiously project on its left- and right-handed components.

Thank you for the reply.

My difficultly is in trying to visualize what chirality physically means. In solid state system, people usually ascribed electron of one chirality to be electron in the conduction band while the opposite chirality belongs to an unoccupied state (hole) in the valence band. Can I then say the electron is left handed, while the hole is right handed. Electron spins clockwise while hole spins anti-clockwise. Is this correct?

Is there an example that describe how electron with different chirality can interacts? Is the electron hole interaction forming an exciton an example of this?
 
  • #4

1. What is chirality?

Chirality refers to the property of an object or particle that makes it non-superposable on its mirror image. In other words, a chiral object or particle is not identical to its mirror image, much like our left and right hands.

2. How do you determine chirality?

Chirality can be determined by looking at the arrangement of atoms or groups around a central atom. If there are four different groups attached to the central atom, the molecule or particle is chiral.

3. What are some examples of chiral particles?

Some common examples of chiral particles include amino acids, sugars, and certain medications. Chirality is also observed in biological molecules such as DNA and proteins.

4. Why is chirality important in chemistry and biology?

Chirality plays a crucial role in many biological processes and chemical reactions. In biology, chiral molecules can have different effects on the body depending on their orientation. In chemistry, chiral molecules can have different chemical and physical properties, which can greatly impact their reactivity and usefulness in various applications.

5. How do we describe particles with chirality?

Particles with chirality are typically described using the R/S system, which assigns a priority to each group attached to the central atom and determines the orientation of the molecule. They can also be described using the D/L system, which is commonly used for sugars and amino acids. Additionally, chirality can be described using optical rotation, where the rotation of polarized light by a chiral molecule is measured.

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