Scalar field

In a physical context, scalar fields are required to be independent of the choice of reference frame.

Mathematically, a scalar field on a region U is a real or complex-valued function or distribution on U.

[1][2] The region U may be a set in some Euclidean space, Minkowski space, or more generally a subset of a manifold, and it is typical in mathematics to impose further conditions on the field, such that it be continuous or often continuously differentiable to some order.

Physically, a scalar field is additionally distinguished by having units of measurement associated with it.

In physics, scalar fields often describe the potential energy associated with a particular force.

A scalar field such as temperature or pressure, where intensity of the field is represented by different hues of colors.
The scalar field of oscillating as increases. Red represents positive values, purple represents negative values, and sky blue represents values close to zero.