quantum field theory (redirected from Relativistic Quantum Mechanics)

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.

Bibliography

See R. P. Feynman, QED (1985); F. J. Yndurain, The Theory of Quark and Gluon Interactions (1993).

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quantum field theory

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. See also grand unified theory, unified field theory.

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quantum field theory [′kwän·təm ′fēld ‚thē·ə·rē]

(quantum mechanics)

Quantum theory of physical systems possessing an infinite number of degrees of freedom, such as the electromagnetic field, gravitation field, or wave fields in a medium.

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Quantum field theory

The quantum-mechanical theory of physical systems whose dynamical variables are local functions of space and time. As distinguished from the quantum mechanics of atoms, quantum field theories describe systems with an infinite number of degrees of freedom. Such theories provide the natural language for describing the interactions and properties of elementary particles, and have proved to be successful in providing the basis for the fundamental theories of the interactions of matter. The present understanding of the basic forces of nature is based on quantum field theories of the strong, weak, electromagnetic, and gravitational interactions. Quantum field theory is also useful in the study of many-body systems, especially in situations where the characteristic length of a system is large compared to its microscopic scale. See Quantum mechanics

Quantum field theory originated in the attempt, in the late 1920s, to unify P. A. M. Dirac's relativistic electron theory and J. C. Maxwell's classical electrodynamics in a quantum theory of interacting photon and electron fields. This effort was completed in the 1950s and was extremely successful. At present the quantitative predictions of the theory are largely limited to perturbative expansions (believed to be asymptotic) in powers of the fine-structure constant. However, because of the extremely small value of this parameter, α = e²/ℏc ≈ 1/137 (where e is the electron charge, ℏ is Planck's constant divided by 2&pgr;, and c is the speed of light), such an expansion is quite adequate for most purposes. The remarkable agreement of the predictions of quantum electrodynamics with high-precision experiments (sometimes to an accuracy of 1 part in 10¹²) provides strong evidence for the validity of the basic tenets of relativistic quantum field theory. See Classical field theory, Electromagnetic radiation, Maxwell's equations, Perturbation (quantum mechanics), Photon, Quantum electrodynamics, Relativistic electrodynamics, Relativistic quantum theory

Quantum field theory also provides the natural framework for the treatment of the weak, strong, and gravitational interactions.

The first of such applications was Fermi's theory of the weak interactions, responsible for radioactivity, in which a hamiltonian was constructed to describe beta decay as a product of four fermion fields, one for each lepton or nucleon. This theory has been superseded by the modern electroweak theory that unifies the weak and the electromagnetic interactions into a common framework. This theory is a generalization of Maxwell's electrodynamics which was the first example of a gauge theory, based on a continuous local symmetry. In the case of electromagnetism the local gauge symmetry is the space-time-dependent change of the phase of a charged field. The existence of massless spin-1 particles, photons, is one of the consequences of the gauge symmetry. The electroweak theory is based on generalizing this symmetry to space-time-dependent transformations of the labels of the fields, based on the group SU(2) × U(1). However, unlike electromagnetism, part of this extended symmetry is not shared by the ground state of the system. This phenomenon of spontaneous symmetry breaking produces masses for all the elementary fermions and for the gauge bosons that are the carriers of the weak interactions, the W^± and Z bosons. (This is known as the Higgs mechanism.) The electroweak theory has been confirmed by many precision tests, and almost all of its essential ingredients have been verified. See Electroweak interaction, Intermediate vector boson, Symmetry breaking, Symmetry laws (physics), Weak nuclear interactions

The application of quantum field theory to the strong or nuclear interactions dates from H. Yukawa's hypothesis that the short-range nuclear forces arise from the exchange of massive particles that are the quanta of local fields coupled to the nucleons, much as the electromagnetic interactions arise from the exchange of massless photons that are the quanta of the electromagnetic field. The modern theory of the strong interactions, quantum chromodynamics, completed in the early 1970s, is also based on a local gauge theory. This is a theory of spin-½ quarks invariant under an internal local SU(3) (color) gauge group. The observed hadrons (such as the proton and neutron) are SU(3) color-neutral bound states of the quarks whose interactions are dictated by the gauge fields (gluons). This theory exhibits almost-free-field behavior of quarks and gluons over distances and times short compared to the size of a hadron (asymptotic freedom), and a strong binding of quarks at large separations that results in the absence of colored states (confinement). See Elementary particle, Gluons, Meson, Quantum chromodynamics, Quarks

Quantum field theory has been tested down to distances of 10^-20 m. There appears to be no reason why it should not continue to work down to Planck's length, (Gℏ/c³)^1/2 ≈ 10^-35 m (where G is the gravitational constant), where the quantum effects of gravity become important. In the case of gravity, A. Einstein's theory of general relativity already provides a very successful classical field theory. However, the union of quantum mechanics and general relativity raises conceptual problems that seem to call for a radical reexamination of the foundations of quantum field theory. See Fundamental interactions, Gravitation, Quantum gravitation, Relativity