.In, quantum field theory ( QFT) is a theoretical framework that combines, and: xi (but notably not 's description of gravity) and is used to construct of (in ) and (in ).QFT treats particles as (also called ) of their underlying, which are—in a sense—more fundamental than the basic particles. Interactions between particles are described by interaction terms in the involving their corresponding fields. Each interaction can be visually represented by, which are formal computational tools, in the process of relativistic. Contents.History As a successful theoretical framework today, quantum field theory emerged from the work of generations of theoretical physicists spanning much of the 20th century. Its development began in the 1920s with the description of interactions between and, culminating in the first quantum field theory —. A major theoretical obstacle soon followed with the appearance and persistence of various infinities in perturbative calculations, a problem only resolved in the 1950s with the invention of the procedure.
A second major barrier came with QFT's apparent inability to describe the and, to the point where some theorists called for the abandonment of the field theoretic approach. The development of and the completion of the in the 1970s led to a renaissance of quantum field theory.Theoretical background. Of the: six types of matter, four types of that carry, as well as the, which endow elementary particles with mass.In 1954, and generalised the of QED, leading to (also known as Yang-Mills theories), which are based on more complicated local.: 5 In QED, (electrically) charged particles interact via the exchange of photons, while in non-Abelian gauge theory, particles carrying a new type of ' interact via the exchange of massless. Unlike photons, these gauge bosons themselves carry charge.: 32developed a non-Abelian gauge theory that unified the electromagnetic and weak interactions in 1960. In 1964, and arrived at the same theory through a different path. This theory, nevertheless, was non-renormalizable., and proposed in 1964 that the gauge symmetry in Yang-Mills theories could be broken by a mechanism called, through which originally massless gauge bosons could acquire mass.: 5-6By combining the earlier theory of Glashow, Salam, and Ward with the idea of spontaneous symmetry breaking, wrote down in 1967 a theory describing between all and the effects of the.
His theory was at first mostly ignored,: 6 until it was brought back to light in 1971 by 's proof that non-Abelian gauge theories are renormalizable. The electroweak theory of Weinberg and Salam was extended from leptons to in 1970 by Glashow, and, marking its completion., and discovered in 1971 that certain phenomena involving the could also be explained by non-Abelian gauge theory. (QCD) was born.
In 1973, and showed that non-Abelian gauge theories are ', meaning that under renormalization, the coupling constant of the strong interaction decreases as the interaction energy increases. (Similar discoveries had been made numerous times previously, but they had been largely ignored.): 11 Therefore, at least in high-energy interactions, the coupling constant in QCD becomes sufficiently small to warrant a perturbative series expansion, making quantitative predictions for the strong interaction possible.: 32These theoretical breakthroughs brought about a renaissance in QFT. The full theory, which includes the electroweak theory and chromodynamics, is referred to today as the of elementary particles. The Standard Model successfully describes all except, and its many predictions have been met with remarkable experimental confirmation in subsequent decades.: 3 The, central to the mechanism of spontaneous symmetry breaking, was finally detected in 2012 at, marking the complete verification of the existence of all constituents of the Standard Model. Other developments The 1970s saw the development of non-perturbative methods in non-Abelian gauge theories. The was discovered by 't Hooft and, by and, and by Polyakov et al.
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These objects are inaccessible through perturbation theory.: 4also appeared in the same period. The first supersymmetric QFT in four dimensions was built by and in 1970, but their result failed to garner widespread interest due to the. Supersymmetry only took off in the theoretical community after the work of and in 1973.: 7Among the four fundamental interactions, gravity remains the only one that lacks a consistent QFT description. Various attempts at a theory of led to the development of,: 6 itself a type of two-dimensional QFT with. And first proposed in 1974 that string theory could be the quantum theory of gravity. Condensed matter physics Although quantum field theory arose from the study of interactions between elementary particles, it has been successfully applied to other physical systems, particularly to in.Historically, the Higgs mechanism of spontaneous symmetry breaking was a result of 's application of theory to elementary particles, while the concept of renormalization came out of the study of second-order in matter.Soon after the introduction of photons, Einstein performed the quantization procedure on vibrations in a crystal, leading to the first —. Lev Landau claimed that low-energy excitations in many condensed matter systems could be described in terms of interactions between a set of quasiparticles.
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The Feynman diagram method of QFT was naturally well suited to the analysis of various phenomena in condensed matter systems.Gauge theory is used to describe the quantization of in superconductors, the in the, as well as the relation between frequency and voltage in the AC. Principles For simplicity, are used in the following sections, in which the ħ and the c are both set to one.Classical fields.