field theory

field theory

In mathematics, the study of the structure of a set of objects (e.g., numbers) with two combining operations (e.g., addition and multiplication). Such a system, known as a field, must satisfy certain properties: associative law, commutative law, distributive law, an additive identity (“zero”), a muliplicative identity (“one”), additive inverses (see inverse function), and multiplicative inverses for nonzero elements. The sets of rational numbers, real numbers, and complex numbers are fields under ordinary addition and multiplication. The investigation of polynomial equations and their solutions led to the development of field theory.

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field theory [′fēld ‚thē·ə·rē]

(mathematics)

The study of fields and their extensions.

(physics)

A theory in which the basic quantities are fields; classically the equations governing the fields may be given; in quantum field theory the commutation rules satisfied by the field operators also are specified.

(psychology)

A psychological theory that emphasizes the importance of interactions between events in an individual's environment.