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# Chirality

## Layman

Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.

## Student

Chirality arises as a quantum number related to the Lorentz group. Form the representation theory of the Lorentz group, we know that the corresponding Lie algebra, can be interpreted as two copies of the $SU(2)$ Lie algebra $\mathfrak{su}(2)$. Therefore, we labelled each representation by two numbers: $j_L$ and $j_R$ which indicate which $\mathfrak{su}(2)$ representations are used to construct the Lorentz algebra representations. For example, the label $(\frac{1}{2},0)$ means that we used to fundamental representation for one $\mathfrak{su}(2)$ and the trivial, one-dimensional representation for the other $\mathfrak{su}(2)$.

A quantum field (or particle) that transforms according to the $(\frac{1}{2},0)$ representation is called left-chiral, and a quantum field (or particle) that transforms according to the $(0,\frac{1}{2})$ representation is called right-chiral.

## Researcher

The motto in this section is: the higher the level of abstraction, the better.
Common Question 1
Common Question 2

Example1
Example2: