Vector under Chiral transformation

In summary, the conversation discusses the transformation of vectors under chiral transformations. It is shown that a vector, represented as $$V^\mu$$, can be expressed as $$\bar{\psi}\gamma^\mu\psi$$ under this transformation. This also applies to the derivative operator $$\partial_\mu$$, which can be written as $$\bar{\psi}\gamma^\mu\psi$$. The person asking the question is looking for further clarification or rewording on this topic.
  • #1
PhyAmateur
105
2
Was reading how do vectors transform under chiral transformation and found the following:

If $$V^\mu$$ is a vector; set $$ V^\mu = \bar{\psi} \gamma^\mu \psi= $$

$$\bar{\psi}\gamma^\mu e^{-i\alpha\gamma^5}e^{i\alpha\gamma^5}\psi =$$
$$\bar{\psi}\gamma^\mu\psi = V^\mu $$

My questions are why is it that vector takes the form $$V^\mu = \bar{\psi}\gamma^\mu\psi$$ and does the same thing apply to $$\partial_\mu$$ I mean is $$\partial_\mu$$ written as $$\bar{\psi}\gamma^\mu\psi$$ ?
 
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  • #2
Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
 

FAQ: Vector under Chiral transformation

1. What is a vector under chiral transformation?

A vector under chiral transformation refers to a mathematical concept where a vector undergoes a transformation that preserves its magnitude but changes its direction. This type of transformation is commonly found in quantum field theory and is used to describe the behavior of particles with spin.

2. How does chiral transformation affect the properties of a vector?

Chiral transformation affects the properties of a vector by changing its orientation in space. This can result in different physical properties and behaviors of the vector, such as its spin and polarization. Chiral transformation is also known to affect the interactions between particles and can lead to new physical phenomena.

3. Is chiral transformation the same as mirror symmetry?

No, chiral transformation is not the same as mirror symmetry. While both concepts involve changes in orientation, chiral transformation specifically refers to a transformation that involves rotations and reflections, while mirror symmetry refers to an exact reflection of an object or system.

4. What is the difference between chiral and achiral vectors?

Chiral vectors are those that are transformed under chiral transformation, meaning that their orientation changes. Achiral vectors, on the other hand, are those that do not change under chiral transformation and maintain their orientation. Achiral vectors are also known as invariant vectors.

5. In what fields of science is chiral transformation commonly used?

Chiral transformation is commonly used in the fields of quantum mechanics, particle physics, and chemistry. It is also used in materials science for the study of crystal structures and in biology for the study of biomolecules and their interactions.

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