Michael Faraday coined the English term "field" in 1845.

This description of fields remains to this day. The theory of classical electromagnetism was completed in 1864 with Maxwell's equations, which described the relationship between the electric field, the magnetic field, electric current, and electric charge.

Building on this idea, Albert Einstein proposed in 1905 an explanation for the photoelectric effect, that light is composed of individual packets of energy called photons (the quanta of light).

This implied that the electromagnetic radiation, while being waves in the classical electromagnetic field, also exists in the form of particles. In 1913, Niels Bohr introduced the Bohr model of atomic structure, wherein electrons within atoms can only take on a series of discrete, rather than continuous, energies.

Its development began in the 1920s with the description of interactions between light and electrons, culminating in the first quantum field theory—quantum electrodynamics.

In 1924, Louis de Broglie proposed the hypothesis of wave–particle duality, that microscopic particles exhibit both wave-like and particle-like properties under different circumstances.

Uniting these scattered ideas, a coherent discipline, quantum mechanics, was formulated between 1925 and 1926, with important contributions from Max Planck, Louis de Broglie, Werner Heisenberg, Max Born, Erwin Schrödinger, Paul Dirac, and Wolfgang Pauli. In the same year as his paper on the photoelectric effect, Einstein published his theory of special relativity, built on Maxwell's electromagnetism.

Uniting these scattered ideas, a coherent discipline, quantum mechanics, was formulated between 1925 and 1926, with important contributions from Max Planck, Louis de Broglie, Werner Heisenberg, Max Born, Erwin Schrödinger, Paul Dirac, and Wolfgang Pauli. In the same year as his paper on the photoelectric effect, Einstein published his theory of special relativity, built on Maxwell's electromagnetism.

With the exclusion of interactions, however, such a theory was yet incapable of making quantitative predictions about the real world. In his seminal 1927 paper The quantum theory of the emission and absorption of radiation, Dirac coined the term quantum electrodynamics (QED), a theory that adds upon the terms describing the free electromagnetic field an additional interaction term between electric current density and the electromagnetic vector potential.

Nonetheless, the application of higher-order perturbation theory was plagued with problematic infinities in calculations. In 1928, Dirac wrote down a wave equation that described relativistic electrons—the Dirac equation.

It was between 1928 and 1930 that Jordan, Eugene Wigner, Heisenberg, Pauli, and Enrico Fermi discovered that material particles could also be seen as excited states of quantum fields.

Atomic nuclei do not contain electrons per se, but in the process of decay, an electron is created out of the surrounding electron field, analogous to the photon created from the surrounding electromagnetic field in the radiative decay of an excited atom. It was realized in 1929 by Dirac and others that negative energy states implied by the Dirac equation could be removed by assuming the existence of particles with the same mass as electrons but opposite electric charge.

It was between 1928 and 1930 that Jordan, Eugene Wigner, Heisenberg, Pauli, and Enrico Fermi discovered that material particles could also be seen as excited states of quantum fields.

QFT naturally incorporated antiparticles in its formalism. === Infinities and renormalization === Robert Oppenheimer showed in 1930 that higher-order perturbative calculations in QED always resulted in infinite quantities, such as the electron self-energy and the vacuum zero-point energy of the electron and photon fields, suggesting that the computational methods at the time could not properly deal with interactions involving photons with extremely high momenta.

Building on this idea, Fermi proposed in 1932 an explanation for beta decay known as Fermi's interaction.

Indeed, the evidence for positrons was discovered in 1932 by Carl David Anderson in cosmic rays.

It was not until 20 years later that a systematic approach to remove such infinities was developed. A series of papers was published between 1934 and 1938 by Ernst Stueckelberg that established a relativistically invariant formulation of QFT.

Unfortunately, such achievements were not understood and recognized by the theoretical community. Faced with these infinities, John Archibald Wheeler and Heisenberg proposed, in 1937 and 1943 respectively, to supplant the problematic QFT with the so-called S-matrix theory.

It was not until 20 years later that a systematic approach to remove such infinities was developed. A series of papers was published between 1934 and 1938 by Ernst Stueckelberg that established a relativistically invariant formulation of QFT.

Unfortunately, such achievements were not understood and recognized by the theoretical community. Faced with these infinities, John Archibald Wheeler and Heisenberg proposed, in 1937 and 1943 respectively, to supplant the problematic QFT with the so-called S-matrix theory.

In 1945, Richard Feynman and Wheeler daringly suggested abandoning QFT altogether and proposed action-at-a-distance as the mechanism of particle interactions. In 1947, Willis Lamb and Robert Retherford measured the minute difference in the 2S1/2 and 2P1/2 energy levels of the hydrogen atom, also called the Lamb shift.

In 1947, Stueckelberg also independently developed a complete renormalization procedure.

In 1945, Richard Feynman and Wheeler daringly suggested abandoning QFT altogether and proposed action-at-a-distance as the mechanism of particle interactions. In 1947, Willis Lamb and Robert Retherford measured the minute difference in the 2S1/2 and 2P1/2 energy levels of the hydrogen atom, also called the Lamb shift.

Using source theory, Schwinger was able to calculate the anomalous magnetic moment of the electron, which he had done in 1947, but this time with no ‘distracting remarks’ about infinite quantities. Schwinger also applied source theory to his QFT theory of gravity, and was able to reproduce all four of Einstein’s classic results: gravitational red shift, deflection and slowing of light by gravity, and the perihelion precession of Mercury.

It was a mutual loss, for both Schwinger and the community were the losers. === Non-renormalizability === Given the tremendous success of QED, many theorists believed, in the few years after 1949, that QFT could soon provide an understanding of all microscopic phenomena, not only the interactions between photons, electrons, and positrons.

Dyson proved in 1949 that this is only possible for a small class of theories called "renormalizable theories", of which QED is an example.

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 renormalization procedure.

However, this method was clumsy and unreliable and could not be generalized to other calculations. The breakthrough eventually came around 1950 when a more robust method for eliminating infinities was developed by Julian Schwinger, Feynman, Freeman Dyson, and Shinichiro Tomonaga.

– "Renormalization theory of quantum electrodynamics: an individual view" by Julian Schwinger This challenge led to six papers on "The theory of quantized fields" published in the Physical Review in 1951-54.

Schwinger === Standard Model === In 1954, Yang Chen-Ning and Robert Mills generalised the local symmetry of QED, leading to non-Abelian gauge theories (also known as Yang–Mills theories), which are based on more complicated local symmetry groups.

Unlike photons, these gauge bosons themselves carry charge. Sheldon Glashow developed a non-Abelian gauge theory that unified the electromagnetic and weak interactions in 1960.

In 1964, Abdus Salam and John Clive Ward arrived at the same theory through a different path.

In fact, he devoted his Nobel speech in 1965 to describing this work, just as Einstein had talked about Relativity in his Nobel speech and not the photoelectric effect theory that he got the award for. The relativistic quantum theory of fields was born some thirty-five years ago through the paternal efforts of Dirac, Heisenberg, Pauli and others.

For more than a decade he and his students had been nearly the only exponents of field theory, but in 1966 he found a way around the problem of the infinities with a new method he called source theory.

The development of gauge theory and the completion of the Standard Model in the 1970s led to a renaissance of quantum field theory. === Theoretical background === Quantum field theory is the result of the combination of classical field theory, quantum mechanics, and special relativity.

The electroweak theory of Weinberg and Salam was extended from leptons to quarks in 1970 by Glashow, John Iliopoulos, and Luciano Maiani, marking its completion. Harald Fritzsch, Murray Gell-Mann, and Heinrich Leutwyler discovered in 1971 that certain phenomena involving the strong interaction could also be explained by non-Abelian gauge theory.

The Higgs boson, central to the mechanism of spontaneous symmetry breaking, was finally detected in 2012 at CERN, 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 first supersymmetric QFT in four dimensions was built by Yuri Golfand and Evgeny Likhtman in 1970, but their result failed to garner widespread interest due to the Iron Curtain.

His theory was at first mostly ignored, until it was brought back to light in 1971 by Gerard 't Hooft's proof that non-Abelian gauge theories are renormalizable.

The electroweak theory of Weinberg and Salam was extended from leptons to quarks in 1970 by Glashow, John Iliopoulos, and Luciano Maiani, marking its completion. Harald Fritzsch, Murray Gell-Mann, and Heinrich Leutwyler discovered in 1971 that certain phenomena involving the strong interaction could also be explained by non-Abelian gauge theory.

In 1973, David Gross, Frank Wilczek, and Hugh David Politzer showed that non-Abelian gauge theories are "asymptotically free", meaning that under renormalization, the coupling constant of the strong interaction decreases as the interaction energy increases.

Supersymmetry only took off in the theoretical community after the work of Julius Wess and Bruno Zumino in 1973. Among the four fundamental interactions, gravity remains the only one that lacks a consistent QFT description.

The Higgs boson, central to the mechanism of spontaneous symmetry breaking, was finally detected in 2012 at CERN, 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.

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