In
mathematics and
physics, a
scalar field associates a
scalar value to every point in a space. The scalar may either be a
mathematical number or a
physical quantity. Scalar fields are required to be coordinate-independent, meaning that any two observers using the same units will agree on the value of the scalar field at the same absolute point in space (or
spacetime) regardless of their respective points of origin. Examples used in physics include the
temperature distribution throughout space, the
pressure distribution in a fluid, and spin-zero quantum fields, such as the
Higgs field. These fields are the subject of
scalar field theory.