tensor density वाक्य
उदाहरण वाक्य
मोबाइल
- The construction of tensor densities is a'twisting'at the cocycle level.
- As applied to tensor densities, it " does " make a difference.
- More generally, any tensor density is the product of an ordinary tensor with a scalar density of the appropriate weight.
- With this choice, classical densities, like charge density, will be represented by tensor densities of weight + 1.
- Such a connection ? immediately defines a covariant derivative not only on the tangent bundle, but on vector bundles tensor densities.
- This allows one to define the concept of "'tensor density "', a'twisted'type of tensor field.
- This tensor density is uniquely characterized by its conformal properties coupled with the demand that it be differentiable for arbitrary metrics, as shown by.
- Note that these classifications elucidate the different ways that tensor densities may transform somewhat pathologically under orientation-" reversing " coordinate transformations.
- Regardless of their classifications into these types, there is only one way that tensor densities transform under orientation-" preserving " coordinate transformations.
- Also, the specific term " symbol " emphasizes that it is not a tensor because of how it transforms between coordinate systems, however it can be interpreted as a tensor density.
- Before we state the next difficulty we should give a definition; a tensor density of weight W transforms like an ordinary tensor, except that in addition the W th power of the Jacobian,
- The bundle of densities cannot seriously be defined'at a point'; and therefore a limitation of the contemporary mathematical treatment of tensors is that tensor densities are defined in a roundabout fashion.
- The Cotton tensor can be regarded as a vector valued 2-form, and for " n " = 3 one can use the Hodge star operator to convert this into a second order trace free tensor density
- The hyperdeterminant can be written in a more compact form using the Einstein convention for summing over indices and the Levi-Civita symbol which is an alternating tensor density with components ? ij specified by ? 00 = ? 11 = 0, ? 01 = " ? 10 = 1:
- A " tensor density " is the special case where " L " is the bundle of " densities on a manifold ", namely the determinant bundle of the cotangent bundle . ( To be strictly accurate, one should also apply the absolute value to the transition functions this makes little difference for an orientable manifold . ) For a more traditional explanation see the tensor density article.
- A " tensor density " is the special case where " L " is the bundle of " densities on a manifold ", namely the determinant bundle of the cotangent bundle . ( To be strictly accurate, one should also apply the absolute value to the transition functions this makes little difference for an orientable manifold . ) For a more traditional explanation see the tensor density article.
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