Spinor Lie Derivative

The Lie derivative of a spinor psi is defined by


where psi^~_t is the image of psi 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 psi is given explicitly by

 L_Xpsi=X^adel _apsi-1/8(del _aX_b-del _bX_a)gamma^agamma^bpsi,

where gamma^a and gamma^b are Dirac matrices (Choquet-Bruhat and DeWitt-Morette 2000).

See also

Covariant Derivative, Dirac Matrices, Lie Derivative, Spinor

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Choquet-Bruhat, Y. and DeWitt-Morette, C. Analysis, Manifolds and Physics, Part II: 92 Applications, rev. ed. Amsterdam, Netherlands: North-Holland, 2000.

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Spinor Lie Derivative

Cite this as:

Weisstein, Eric W. "Spinor Lie Derivative." From MathWorld--A Wolfram Web Resource.

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