Everything about Tensor Density totally explained
A
tensor density transforms as a
tensor, except that it's additionally multiplied or
weighted by a power of the
Jacobian determinant.
For example, a rank-3 tensor density of weight W transforms as:
» is the Jacobian determinant.
A tensor density of weight zero is an ordinary tensor.
A distinction is made between
odd tensor densities, in which (as here) the term attributable to the determinant may be negative, and
even tensor densities which have a power of the
absolute value of the determinant, or an even power of it, in the transformation rule.
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