Definition:Field (Physics)

Definition

A field, in the context of physics, is a region of space which is acted on by a point-function.

That is, in which a physical quantity is associated with every point of spacetime.

The physical quantity in question may be either in vector or scalar form.

Scalar Field

Let $F$ be a field which acts on a region of space $S$.

Let the point-function giving rise to $F$ be a scalar quantity.

Then $F$ is a scalar field.

Vector Field

Let $F$ be a field which acts on a region of space $S$.

Let the point-function giving rise to $F$ be a vector quantity.

Then $F$ is a vector field.