Editing Quantum field theory (section)

===Quantum electrodynamics===
Quantum field theory naturally began with the study of electromagnetic interactions, as the electromagnetic field was the only known classical field as of the 1920s.{{r|shifman|page1=1}}

Through the works of Born, Heisenberg, and [[Pascual Jordan]] in 1925–1926, a quantum theory of the free electromagnetic field (one with no interactions with matter) was developed via [[canonical quantization]] by treating the electromagnetic field as a set of [[quantum harmonic oscillator]]s.{{r|shifman|page1=1}} With the exclusion of interactions, however, such a theory was yet incapable of making quantitative predictions about the real world.{{r|weinberg|page1=22}}

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 four-potential|electromagnetic vector potential]]. Using first-order [[perturbation theory (quantum mechanics)|perturbation theory]], he successfully explained the phenomenon of spontaneous emission. According to the [[uncertainty principle]] in quantum mechanics, quantum harmonic oscillators cannot remain stationary, but they have a non-zero minimum energy and must always be oscillating, even in the lowest energy state (the [[ground state]]). Therefore, even in a perfect [[vacuum]], there remains an oscillating electromagnetic field having [[zero-point energy]]. It is this [[quantum fluctuation]] of electromagnetic fields in the vacuum that "stimulates" the spontaneous emission of radiation by electrons in atoms. Dirac's theory was hugely successful in explaining both the emission and absorption of radiation by atoms; by applying second-order perturbation theory, it was able to account for the [[scattering]] of photons, [[resonance fluorescence]] and non-relativistic [[Compton scattering]]. Nonetheless, the application of higher-order perturbation theory was plagued with problematic infinities in calculations.<ref name="weisskopf" />{{rp|71}}

In 1928, Dirac wrote down a [[wave equation]] that described relativistic electrons: the [[Dirac equation]]. It had the following important consequences: the [[Spin (physics)|spin]] of an electron is 1/2; the electron [[g-factor (physics)|''g''-factor]] is 2; it led to the correct Sommerfeld formula for the [[fine structure]] of the [[hydrogen atom]]; and it could be used to derive the [[Klein–Nishina formula]] for relativistic Compton scattering. Although the results were fruitful, the theory also apparently implied the existence of negative energy states, which would cause atoms to be unstable, since they could always decay to lower energy states by the emission of radiation.<ref name="weisskopf" />{{rp|71–72}}

The prevailing view at the time was that the world was composed of two very different ingredients: material particles (such as electrons) and [[Field (physics)#Quantum fields|quantum fields]] (such as photons). Material particles were considered to be eternal, with their physical state described by the probabilities of finding each particle in any given region of space or range of velocities. On the other hand, photons were considered merely the [[excited state]]s of the underlying quantized electromagnetic field, and could be freely created or destroyed. 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. Just as photons are excited states of the quantized electromagnetic field, so each type of particle had its corresponding quantum field: an electron field, a proton field, etc. Given enough energy, it would now be possible to create material particles. Building on this idea, Fermi proposed in 1932 an explanation for [[beta decay]] known as [[Fermi's interaction]]. [[Atomic nucleus|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.{{r|weinberg|page1=22–23}}

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. This not only ensured the stability of atoms, but it was also the first proposal of the existence of [[antimatter]]. Indeed, the evidence for [[positron]]s was discovered in 1932 by [[Carl David Anderson]] in [[cosmic ray]]s. With enough energy, such as by absorbing a photon, an electron-positron pair could be created, a process called [[pair production]]; the reverse process, annihilation, could also occur with the emission of a photon. This showed that particle numbers need not be fixed during an interaction. Historically, however, positrons were at first thought of as "holes" in an infinite electron sea, rather than a new kind of particle, and this theory was referred to as the [[Dirac hole theory]].<ref name="weisskopf" />{{rp|72}}{{r|weinberg|page1=23}} QFT naturally incorporated antiparticles in its formalism.{{r|weinberg|page1=24}}