Chiral symmetry

A chiral phenomenon is one that is not identical to its mirror image (see the article on mathematical chirality). The spin of a particle may be used to define a handedness, or helicity, for that particle, which, in the case of a massless particle, is the same as chirality. A symmetry transformation between the two is called parity. Invariance under parity by a Dirac fermion is called chiral symmetry.

An experiment on the weak decay of cobalt-60 nuclei carried out by Chien-Shiung Wu and collaborators in 1957 demonstrated that parity is not a symmetry of the universe.

The helicity of a particle is right-handed if the direction of its spin is the same as the direction of its motion. It is left-handed if the directions of spin and motion are opposite. By convention for rotation, a standard clock, with its spin vector defined by the rotation of its hands, tossed with its face directed forwards, has left-handed helicity. Mathematically, helicity is the sign of the projection of the spin vector onto the momentum vector: left is negative, right is positive.

The chirality of a particle is more abstract. It is determined by whether the particle transforms in a right- or left-handed representation of the Poincaré group. (However, some representations, such as Dirac spinors, have both right- and left-handed components. In cases like this, we can define projection operators that project out either the right or left hand components and discuss the right- and left-handed portions of the representation.)

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