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advanced_notions:chirality

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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.

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.

The motto in this section is: *the higher the level of abstraction, the better*.

- Common Question 1

- Common Question 2

- Example1

- Example2:

advanced_notions/chirality.1508748548.txt.gz · Last modified: 2017/12/04 08:01 (external edit)

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