a field of scalars
a function from R n to R
a generalisation of a surface function in dimension
a real valued function over a manifold
a scalar-valued function of position, again independent of the coordinate system
In mathematics and physics, a scalar field associates a scalar value, which can be either mathematical in definition, or physical, to every point in space. Scalar fields are often used in physics, for instance to indicate the temperature distribution throughout space, or the air pressure. In mathematics, or more specifically, differential geometry, the set of functions defined on a manifold define the commutative ring of functions.