Unformatted text preview: “absolute” constants. This remark is very important because in physics we also use quantities that transform like relative tensors. A reZative tensor of weight w is an object with components whose transformation law differs from the tensor transformation law by the appearance of the Jacobian to the wth power as a factor. Thus, (3) (4) are the transformation laws for a relative scalar field of weight w and a relative contravariant vector field of weight w, respectively. If w = 0, we have the previous notion of a tensor field. Whether an object is a tensor or a relative tensor is often a matter of definition. As an example, consider the total mass enclosed in a volume expressed in terms of density. Let xi be rectangular coordinates which are transformed into curvilinear coordinates 0,. We have (5)...
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- Fall '05
- Vector Space, Tensor, Covariance and contravariance of vectors, Tensor field, Metric tensor