Why is it interesting?

Layman

Positive and negative chirality fermions are often described as being right-handed or left-handed, respectively;if one shines a beam of positive chirality fermions (particles described math-matically as sections of S+) into a block of matter, it will begin to spin in a right-handed sense." from Geometry and Physics by E. Witten

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

Common Question 1

Common Question 2

Examples

Example1

Example2:

History