The Lie derivative of a spinor 
is defined by
 |
where 
is the image of 
by a one-parameter group of isometries with 
its generator. For a vector field 
and a covariant
derivative 
,
the Lie derivative of 
is given explicitly by
 |
where 
and 
are Dirac matrices (Choquet-Bruhat and DeWitt-Morette
2000).
