tensor field वाक्य
उदाहरण वाक्य
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- On a manifold, a tensor field will typically have multiple indices, of two sorts.
- The covariant derivative of a tensor field is presented as an extension of the same concept.
- Nowadays, one recognizes this as a single antisymmetric 2nd-rank tensor field in spacetime.
- The divergence of a continuously differentiable second-order tensor field is a first-order tensor field:
- The divergence of a continuously differentiable second-order tensor field is a first-order tensor field:
- Suggestively, replacing the vector field with a rank-tensor field, this can be generalized to:
- In general, one can define various divergence operations on higher-rank tensor fields, as follows.
- More precisely, a tensor field assigns to any given point of the manifold a tensor in the space
- This handles the formulation of variation of a tensor field " along " a vector field.
- The components of this derivative of a tensor field transform covariantly, and hence form another tensor field.
- The components of this derivative of a tensor field transform covariantly, and hence form another tensor field.
- This table shows important examples of tensors, including both tensors on vector spaces and tensor fields on manifolds.
- In other words, a two-form is a skew-symmetric covariant tensor field of order 2.
- This tensor simplifies and reduces Maxwell's equations as four vector calculus equations into two tensor field equations.
- Characterized by their spin, a bosonic field can be scalar fields, vector fields and even tensor fields.
- The above equations and definitions can be extended to vector fields and more generally tensor fields and spinor fields.
- We can describe geometries in general relativity in terms of a tetrad field instead of the usual metric tensor field.
- One would then obtain a pseudo-Riemannian metric tensor field g \, of signature ( 3, 1 ) by
- The Lie derivative is the rate of change of a vector or tensor field along the flow of another vector field.
- 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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