Tensor density

In differential geometry, a tensor density or relative tensor is a generalization of the tensor field concept. A tensor density transforms as a tensor field when passing from one coordinate system to another (see tensor field), except that it is additionally multiplied or weighted by a power W of the Jacobian determinant of the coordinate transition function or its absolute value. A tensor density with a single index is called a vector density. A distinction is made among (authentic) tensor densities, pseudotensor densities, even tensor densities and odd tensor densities. Sometimes tensor densities with a negative weight W are called tensor capacity.[1][2][3] A tensor density can also be regarded as a section of the tensor product of a tensor bundle with a density bundle.

  1. ^ Weinreich, Gabriel (July 6, 1998). Geometrical Vectors. University of Chicago Press. pp. 112, 115. ISBN 978-0226890487.
  2. ^ Papastavridis, John G. (Dec 18, 1998). Tensor Calculus and Analytical Dynamics. CRC Press. ISBN 978-0849385148.
  3. ^ Ruiz-Tolosa, Castillo, Juan R., Enrique (30 Mar 2006). From Vectors to Tensors. Springer Science & Business Media. ISBN 978-3540228875.{{cite book}}: CS1 maint: multiple names: authors list (link)