Weyl equation

The Weyl equation of particle physics, named after Hermann Weyl, is the Dirac equation for massless particles with spin -1 / 2 It is used in the description of the weak interaction.

The representation of the Lorentz group on Dirac spinors is reducible. In a suitable representation of the Dirac matrices, the Weyl representation, transform the first two and the last two separated components of the 4 - spinors,

The 2 - spinors and are the left - and right-handed Weyl spinors.

They are coupled to the Dirac equation for a free Spin-1/2-Teilchen by the mass,

Here are the Pauli matrices.

Disappearance of mass, so the Dirac equation decomposes into a respective Weyl equation for the left - and right-handed spinor

For a description of the weak interaction is important that the left - and right-handed spinors different, but Lorentz invariant, can be coupled to vector fields. The coupling is caused by replacing the derivatives by covariant derivatives called

The components of the vector fields and matrices denoted ( representing the Lie algebra of the gauge group ). The number is the coupling constant. The representation matrices can be different for the left-handed and right-handed spinors. In the weak interaction disappear when the right-handed spinors, the matrices, the right-handed spinors have no weak interaction. Since the coupling of left-handed and right-handed spinors is different, it is also called chiral coupling.

• Particle Physics