Chirality (physics)

Chirality (Physics)

Chirality (physics)

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A chiral phenomenon is one that is not identical to its mirror image (see Chirality). The spin of a particle may be used to define a handedness (aka chirality) for that particle. 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.

Chirality and helicity

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, 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.)

For massless particles—such as the photon, the gluon, and the (hypothetical) graviton—chirality is the same as......
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