Field theory

A field theory is a mathematical description of physical phenomena which describes the behavior of a particle, not only by the physical qualities of the particle itself (e.g., mass, charge, etc.) but also the position of that particle in space relative to other objects. Such descriptions are called "field theories" because the effects of a particle's position exist regardless of the presence of an actual particle, and so describe physical phenomenon at every point in space - such a description is a "field."

History

A "field theory" is based upon the principle of "action-at-a-distance" - that is, the idea that one object can influence another without touching it. The earliest mathematical field theory is the classical theory of gravity, first described by Isaac Newton. He described the force on a particle as related to the product of the particles mass <math>m_1 \ </math> and its distance from another mass, <math>\frac{m_2}{r^2} \ </math>. This is called a field theory because regardless of the first particle, the second gives rise to a "field" everywhere in space which would affect any particle at any position.

Later field theories include James Maxwells theory of electromagnetism, the general theory of relativity, and modern quantum field theory.

Classical field theories, like Newtons, do not include the effects of special relativity. Modern field theories tend to include special relativity in their formulation.