Field

The term field designates a variety of different, closely related concepts in mathematics and physics that have been carried over into everyday language to designate a context or region of influence. In geometry a field is a function that is defined (i.e., has values) at every point of a manifold (smooth continuous surface). Similarly, in physics a field (e.g., an electric, magnetic, or gravitational field) is a function describing a physical quantity (e.g., electric, magnetic, or gravitational influence or forces) at all points of a region of space and time. Sometimes the region that is under the influence of an electric, magnetic, gravitational, or other source or agent is also referred to as a field. A similar and almost equivalent definition of a field in physics, especially in contemporary physics, is as a continuous dynamical system, or a dynamical system with infinite degrees of freedom. Fields are essential to the description of physical phenomena, particularly of the interaction between particles or other physical entities, and to the quantitative and qualitative modeling of forces, especially those that act at a distance without any medium.

See also FIELD THEORIES; GRAVITATION; PHYSICS, QUANTUM

WILLIAM R. STOEGER