Weyl equation
In physics, particularly quantum field theory, the Weyl Equation is a relativistic wave equation for describing massless spin-1/2 particles. It is named after the German physicist Hermann Weyl.
The general equation can be written:
explicitly in SI units:
where
is a vector whose components are the 2 × 2 identity matrix for μ = 0 and the Pauli matrices for μ = 1,2,3, and ψ is the wavefunction - one of the Weyl spinors.
The elements ψL and ψR are respectively the left and right handed Weyl spinors, each with two components. Both have the form
where
is a constant two-component spinor.
Since the particles are massless, i.e. m = 0, the magnitude of momentum p relates directly to the wave-vector k by the De Broglie relations as:
The equation can be written in terms of left and right handed spinors as:
where .
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