In particle physics, the history of quantum field theory starts with its creation by Paul Dirac, when he attempted to quantize the electromagnetic field in the late 1920s. Major advances in the theory were made in the 1940s and 1950s, leading to the introduction of renormalized quantum electrodynamics (QED). The field theory behind QED was so accurate and successful in predictions that efforts were made to apply the same basic concepts for the other forces of nature. Beginning in 1954, the parallel was found by way of gauge theory, leading by the late 1970s, to quantum field models of strong nuclear force and weak nuclear force, united in the modern Standard Model of particle physics.
Efforts to describe gravity using the same techniques have, to date, failed. The study of quantum field theory is still flourishing, as are applications of its methods to many physical problems. It remains one of the most vital areas of theoretical physics today, providing a common language to several different branches of physics.
Early developments Quantum field theory originated in the 1920s from the problem of creating a quantum mechanical theory of the electromagnetic field. In particular, de Broglie in 1924 introduced the idea of a wave description of elementary systems in the following way: "we proceed in this work from the assumption of the existence of a certain periodic phenomenon of a yet to be determined character, which is to be attributed to each and every isolated energy parcel".
In 1925, Werner Heisenberg, Max Born, and Pascual Jordan constructed just such a theory by expressing the field's internal degrees of freedom as an infinite set of harmonic oscillators, and by then utilizing the canonical quantization procedure to these oscillators; their paper was published in 1926. The paper was received on 16 November 1925. [English translation in: This paper was preceded by an earlier one by Born and Jordan published in 1925. () This theory assumed that no electric charges or currents were present and today would be called a free field theory.
The first reasonably complete theory of quantum electrodynamics, which included both the electromagnetic field and electrically charged matter as quantum mechanical objects, was created by Paul Dirac in 1927. This quantum field theory could be used to model important processes such as the emission of a photon by an electron dropping into a quantum state of lower energy, a process in which the number of particles changes—one atom in the initial state becomes an atom plus a photon in the final state. It is now understood that the ability to describe such processes is one of the most important features of quantum field theory.
The final crucial step was Enrico Fermi's theory of β-decay (1934). It was shown that the non-conservation of fermion species is a consequence of second quantization. Creation and annihilation of fermions came to the fore, and it was shown that quantum field theory describes particle decays. Fermi's breakthrough was somewhat foreshadowed in the abstract studies of Soviet physicists, Viktor Ambartsumian and Dmitri Ivanenko, in particular the Ambarzumian–Ivanenko hypothesis of creation of massive particles (1930). The idea was that not only the quanta of the electromagnetic field, photons, but also other particles might emerge and disappear as a result of their interaction with other particles.
Incorporating special relativity It was evident from the beginning that a proper quantum treatment of the electromagnetic field had to somehow incorporate Einstein's relativity theory, which had grown out of the study of classical electromagnetism. This need to put together relativity and quantum mechanics was the second major motivation in the development of quantum field theory.
Pascual Jordan and Wolfgang Pauli showed in 1928Jagdish Mehra, Helmut Rechenberg, The Probability Interpretation and the Statistical Transformation Theory, the Physical Interpretation, and the Empirical and Mathematical Foundations of Quantum Mechanics 1926–1932, Springer, 2000, p. 199. that quantum fields could be made to behave in the way predicted by special relativity during coordinate transformations. Specifically, they showed that the field commutators were Lorentz invariant. Quantum field theory received a further boost from the discovery of the Dirac equation, which was originally formulated and interpreted as a single-particle equation analogous to the Schrödinger equation. Unlike the Schrödinger equation, the Dirac equation satisfies both Lorentz invariance, i.e. the requirements of special relativity, and the rules of quantum mechanics. The Dirac equation took into account the spin-1/2 value of the electron and its magnetic moment, and also provided accurate predictions for the spectra of hydrogen.
The attempt to interpret the Dirac equation as a single-particle equation did not last long, however, and it eventually became apparent that some of its undesirable properties, such as states of negative energy, could be explained by reformulating and reinterpreting the Dirac equation as a true field equation. The quantized "Dirac field" or "electron field" was introduced, with the "solutions of negative energy" pointing to the existence of antiparticles. This work was performed first by Dirac himself with the invention of hole theory in 1930 and by Wendell Furry, Robert Oppenheimer, Vladimir Fock and others.
Erwin Schrödinger, during the same period that he discovered his equation in 1926, also independently found the relativistic generalization of it known as the Klein–Gordon equation but dismissed it since, without spin, it predicted impossible properties for the hydrogen spectrum. Refer also to the work of Oskar Klein and Walter Gordon. All relativistic wave equations that describe spin-zero particles are said to be of the Klein–Gordon type.
Uncertainty, again A subtle and careful analysis in 1933 by Niels Bohr and Léon Rosenfeld showed that there is a fundamental limitation on the ability to simultaneously measure the electric and magnetic field strengths that enter into the description of charges in interaction with radiation, imposed by the uncertainty principle, which must apply to all canonically conjugate quantities. This limitation is crucial for the successful formulation and interpretation of a quantum field theory of photons and electrons (quantum electrodynamics), and indeed, any perturbative quantum field theory. The analysis of Bohr and Rosenfeld explains fluctuations in the values of the electromagnetic field that differ from the classically "allowed" values distant from the sources of the field.
Their analysis was crucial to showing that the limitations and physical implications of the uncertainty principle apply to all dynamical systems, whether fields or material particles. Their analysis also convinced most physicists that any notion of returning to a fundamental description of nature based on classical field theory, such as what Einstein aimed at with his numerous and failed attempts at a classical unified field theory, was simply out of the question. Fields had to be quantized.
Second quantization The third thread in the development of quantum field theory was the need to handle the statistics of many-particle systems consistently and with ease. In 1927, Pascual Jordan tried to extend the canonical quantization of fields to the many-body wave functions of identical particles using a formalism which is known as statistical transformation theory;Don Howard, "Quantum Mechanics in Context: Pascual Jordan's 1936 Anschauliche Quantentheorie" . this procedure is now sometimes called second quantization.Daniel Greenberger, Klaus Hentschel, Friedel Weinert (eds.), Compendium of Quantum Physics: Concepts, Experiments, History and Philosophy, Springer, 2009: "Quantization (First, Second)".Arthur I. Miller, Early Quantum Electrodynamics: A Sourcebook, Cambridge University Press, 1995, p. 18. Dirac is also credited with the invention, as he introduced the key ideas in a 1927 paper.
In 1928, Jordan and Eugene Wigner found that the quantum field describing electrons, or other fermions, had to be expanded using anti-commuting creation and annihilation operators due to the Pauli exclusion principle (see Jordan–Wigner transformation). This thread of development was incorporated into many-body theory and strongly influenced condensed matter physics and nuclear physics. The problem of infinities
Despite its early successes quantum field theory was plagued by several serious theoretical difficulties. Basic physical quantities, such as the self-energy of the electron, the energy shift of electron states due to the presence of the electromagnetic field, gave infinite, divergent contributions—a nonsensical result—when computed using the perturbative techniques available in the 1930s and most of the 1940s.
The electron self-energy problem was already a serious issue in the classical electromagnetic field theory, where the attempt to attribute to the electron a finite size or extent (the classical electron-radius) led immediately to the question of what non-electromagnetic stresses would need to be invoked, which would presumably hold the electron together against the Coulomb repulsion of its finite-sized "parts". The situation was dire, and had certain features that reminded many of the "Rayleigh–Jeans catastrophe".
What made the situation in the 1940s so desperate and gloomy, however, was the fact that the correct ingredients (the second-quantized Maxwell–Dirac field equations) for the theoretical description of interacting photons and electrons were well in place, and no major conceptual change was needed analogous to that which was necessitated by a finite and physically sensible account of the radiative behavior of hot objects, as provided by the Planck radiation law.
Renormalization procedures Improvements in microwave technology made it possible to take more precise measurements of the shift of the levels of a hydrogen atom, now known as the Lamb shift and magnetic moment of the electron. These experiments exposed discrepancies which the theory was unable to explain.
A first indication of a possible way out was given by Hans Bethe in 1947, after attending the Shelter Island Conference. While he was traveling by train from the conference to Schenectady he made the first non-relativistic computation of the shift of the lines of the hydrogen atom as measured by Lamb and Retherford. Despite the limitations of the computation, agreement was excellent. The idea was simply to attach infinities to corrections of mass and charge that were actually fixed to a finite value by experiments. In this way, the infinities get absorbed in those constants and yield a finite result in good agreement with experiments. This procedure was named renormalization.
This "divergence problem" was solved in the case of quantum electrodynamics through the procedure known as renormalization in 1947–49 by Hans Kramers,Kramers presented his work at the 1947 Shelter Island Conference, repeated in 1948 at the Solvay Conference. The latter did not appear in print until the Proceedings of the Solvay Conference, published in 1950 (see Laurie M. Brown (ed.), Renormalization: From Lorentz to Landau (and Beyond), Springer, 2012, p. 53). Kramers' approach was nonrelativistic (see Jagdish Mehra, Helmut Rechenberg, The Conceptual Completion and Extensions of Quantum Mechanics 1932-1941. Epilogue: Aspects of the Further Development of Quantum Theory 1942-1999: Volume 6, Part 2, Springer, 2001, p. 1050). Hans Bethe, Julian Schwinger, Richard Feynman, and Shin'ichiro Tomonaga; the procedure was systematized by Freeman Dyson in 1949. Great progress was made after realizing that all infinities in quantum electrodynamics are related to two effects: the self-energy of the electron/positron, and vacuum polarization.