| 21. | In the special case of inertial frames, the Fermi Walker derivatives reduce to covariant derivatives.
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| 22. | Note that the partial derivatives may be written in terms of covariant derivatives and Christoffel symbols as
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| 23. | Where \ nabla _ \ mu is the general-relativistic covariant derivative of a spinor.
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| 24. | We introduce an arbitrary covariant derivative via
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| 25. | The gauge covariant derivative transforms similarly.
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| 26. | That is we trace the covariant derivative on the " first two " covariant indices.
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| 27. | Ricci calculus is the modern formalism and notation for tensor indices : indicating partial and covariant derivatives.
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| 28. | Of particular note is their concept of a "'dynamical covariant derivative " '.
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| 29. | The symbol \ partial _ k denotes partial derivative, while \ nabla _ k denotes covariant derivative.
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| 30. | The covariant derivative \ nabla _ a is defined to annihilate the tetrad E _ a ^ I.
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