nLab
scalar

Contents

Contents

Idea

Broadly, a scalar quantity is a “basic form of quantity”, in terms of which more sophisticated objects of algebra are defined; and/or a “plain form of quantity”, not subject to non-trivial transformation laws.

Specifically:

These two usages do overlap: The 1-dimensional trivial representation 1Rep k(G)\mathbf{1} \in Rep_k(G) of any symmetry group GG over any ground field kk has as underlying set that ground field itself: 1 kk\mathbf{1} \,\simeq_k\, k.

For instance, the scalar curvature in Riemannian geometry is a scalar(-valued function) in both senses of the word.

References

See also

Last revised on April 6, 2020 at 07:42:57. See the history of this page for a list of all contributions to it.