Weyl equation
Encyclopedia
Mathematical Formulation
- where
-
is the Pauli spin matrixPauli matricesThe Pauli matrices are a set of three 2 × 2 complex matrices which are Hermitian and unitary. Usually indicated by the Greek letter "sigma" , they are occasionally denoted with a "tau" when used in connection with isospin symmetries...
,
and 
are, respectively, right- and left-handed Weyl spinors.
Derivation
The equations are obtained from the Lagrangian densities
By treating the spinor and its conjugate
Hermitian adjoint
In mathematics, specifically in functional analysis, each linear operator on a Hilbert space has a corresponding adjoint operator.Adjoints of operators generalize conjugate transposes of square matrices to infinite-dimensional situations...
(denoted by
) as independent variables, the relevant Weyl equation is obtained.Source: http://aesop.phys.utk.edu/qft/2004-5/2-2.pdf