The Lie derivative of a spinor ψ is defined by ℒ_X ψ(x) = lim_(t->0) (ψ^~_t(x) - ψ(x))/t, where ψ^~_t is the image of ψ by a one-parameter group of isometries with X its generator. For a vector field X^a and a covariant derivative del _a, the Lie derivative of ψ is given explicitly by ℒ_X ψ = X^a del _a ψ - 1/8( del _a X_b - del _b X_a) γ^a γ^b ψ, where γ^a and γ^b are Dirac matrices.

covariant derivative | Dirac matrices | Lie derivative | spinor