| 31. | The components of this derivative of a tensor field transform covariantly, and hence form another tensor field.
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| 32. | This table shows important examples of tensors, including both tensors on vector spaces and tensor fields on manifolds.
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| 33. | In other words, a two-form is a skew-symmetric covariant tensor field of order 2.
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| 34. | This tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations.
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| 35. | Characterized by their spin, a bosonic field can be scalar fields, vector fields and even tensor fields.
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| 36. | The above equations and definitions can be extended to vector fields and more generally tensor fields and spinor fields.
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| 37. | We can describe geometries in general relativity in terms of a tetrad field instead of the usual metric tensor field.
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| 38. | One would then obtain a pseudo-Riemannian metric tensor field g \, of signature ( 3, 1 ) by
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| 39. | The Lie derivative is the rate of change of a vector or tensor field along the flow of another vector field.
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| 40. | The description of tensor fields and operations on them in terms of their components is the focus of the Ricci calculus.
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