quantum field theory, study of the quantum mechanical interaction of elementary particles and fields. Quantum field theory applied to the understanding of electromagnetism is called quantum electrodynamics (QED), and it has proved spectacularly successful in describing the interaction of light with matter. The calculations, however, are often complex. They are usually carried out with the aid of Feynman diagrams (named after American physicist Richard P. Feynman), simple graphs that represent possible variations of interactions and provide an elegant shorthand for precise mathematical equations. Quantum field theory applied to the understanding of the strong interactions between quarks and between protons, neutrons, and other baryons and mesons is called quantum chromodynamics (QCD); QCD has a mathematical structure similar to that of QED.

Attempt to describe all fundamental interactions between elementary particles in terms of a single theoretical framework (a “theory of everything”) based on quantum field theory. So far, the weak force and the electromagnetic force have been successfully united in electroweak theory, and the strong force is described by a similar quantum field theory called quantum chromodynamics. However, attempts to unite the strong and electroweak theories in a grand unified theory have failed, as have attempts at a self-consistent quantum field theory of gravitation.

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Theory that brings quantum mechanics and special relativity together to account for subatomic phenomena. In particular, the interactions of subatomic particles are described in terms of their interactions with fields, such as the electromagnetic field. However, the fields are quantized and represented by particles, such as photons for the electromagnetic field. Quantum electrodynamics is the quantum field theory that describes the interaction of electrically charged particles via electromagnetic fields. Quantum chromodynamics describes the action of the strong force. The electroweak theory, a unified theory of electromagnetic and weak forces, has considerable experimental support, and can likely be extended to include the strong force. Theories that include the gravitational force (see gravitation) are more speculative. Seealso grand unified theory, unified field theory.

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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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