Instruct: Given a question, retrieve documents that answer the question.
Query: When was quantum field theory developed?
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.[8]:1
Abraham–Lorentz force AdS/CFT correspondence Introduction to quantum mechanics Common integrals in quantum field theory Einstein–Maxwell–Dirac equations Form factor (quantum field theory) Green–Kubo relations Green's function (many-body theory) List of quantum field theories Quantization of a field Quantum electrodynamics Quantum field theory in curved spacetime Quantum flavordynamics Quantum hydrodynamics Quantum triviality Relation between Schrödinger's equation and the path integral formulation of quantum mechanics Relationship between string theory and quantum field theory Schwinger–Dyson equation Static forces and virtual-particle exchange Symmetry in quantum mechanics Theoretical and experimental justification for the Schrödinger equation Ward–Takahashi identity Wheeler–Feynman absorber theory Wigner's classification Wigner's theorem
Two classic text-books from the 1960s, James D. Bjorken, Sidney David Drell, "Relativistic Quantum Mechanics" (1964) and J. J. Sakurai, "Advanced Quantum Mechanics" (1967), thoroughly developed the Feynman graph expansion techniques using physically intuitive and practical methods following from the correspondence principle, without worrying about the technicalities involved in deriving the Feynman rules from the superstructure of quantum field theory itself. Although both Feynman's heuristic and pictorial style of dealing with the infinities, as well as the formal methods of Tomonaga and Schwinger, worked extremely well, and gave spectacularly accurate answers, the true analytical nature of the question of "renormalizability", that is, whether ANY theory formulated as a "quantum field theory" would give finite answers, was not worked-out until much later, when the urgency of trying to formulate finite theories for the strong and electro-weak (and gravitational interactions) demanded its solution.
The idea of quantum field theory began in the late 1920s with British physicist [[Paul Dirac]], when he attempted to [[quantization (physics)|quantise]] the [[electromagnetic field]] – a procedure for constructing a quantum theory starting from a classical theory.
It is now believed that quantum mechanics should underlie all physical phenomena, so that a classical field theory should, at least in principle, permit a recasting in quantum mechanical terms; success yields the corresponding quantum field theory. For example, quantizing classical electrodynamics gives quantum electrodynamics. Quantum electrodynamics is arguably the most successful scientific theory; experimental data confirm its predictions to a higher precision (to more significant digits) than any other theory. The two other fundamental quantum field theories are quantum chromodynamics and the electroweak theory.
The application of the new quantum theory to electromagnetism resulted in quantum field theory, which was developed starting around 1930. Quantum field theory has driven the development of more sophisticated formulations of quantum mechanics, of which the ones presented here are simple special cases. 
In collaboration with Nathan Seiberg, Witten established several powerful results in quantum field theories. In their paper on string theory and noncommutative geometry, Seiberg and Witten studied certain noncommutative quantum field theories that arise as limits of string theory. In another well-known paper, they studied aspects of supersymmetric gauge theory. The latter paper, combined with Witten's earlier work on topological quantum field theory, led to developments in the topology of smooth 4-manifolds, in particular the notion of Seiberg–Witten invariants.
In mathematical physics, noncommutative quantum field theory (or quantum field theory on noncommutative spacetime) is an application of noncommutative mathematics to the spacetime of quantum field theory that is an outgrowth of noncommutative geometry and index theory in which the coordinate functions are noncommutative. One commonly studied version of such theories has the "canonical" commutation relation:
In 1990, Moffat proposed a finite, non-local quantum field theory. The theory was developed extensively by Evens, Moffat, Kleppe and Woodard in 1991. In subsequent work, Moffat proposed this theory as an alternative to the standard electroweak unification of electromagnetism and the weak nuclear interactions. Moffat's theory is a quantum field theory with a non-local term in the field Lagrangian. The theory is gauge invariant and it is finite to all orders of perturbation theory. For the standard model it can solve the Higgs boson mass hierarchy naturalness problem. It also leads to a finite quantum gravity theory.University of Toronto press releases re Moffat:
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 1928 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). A further boost for quantum field theory came with the discovery of the Dirac equation, which was originally formulated and interpreted as a single-particle equation analogous to the Schrödinger equation, but unlike the Schrödinger equation, the Dirac equation satisfies both the Lorentz invariance, that is, the requirements of special relativity, and the rules of quantum mechanics. 
The Dirac equation accommodated the spin-1/2 value of the electron and accounted for its magnetic moment as well as giving accurate predictions for the spectra of hydrogen.
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 oscillators.[8]:1 With the exclusion of interactions, however, such a theory was yet incapable of making quantitative predictions about the real world.[3]:22
Further development of quantum field theory changed the focus of searching for unified field theory from classical to quantum description. Because of that, many theoretical physicists gave up looking for a classical unified field theory. Quantum field theory would include unification of other two fundamental forces of nature, strong and weak nuclear force which act on subatomic level.
Quantum field theory on curved (non-Minkowskian) backgrounds, while not a full quantum theory of gravity, has shown many promising early results. In an analogous way to the development of quantum electrodynamics in the early part of the 20th century (when physicists considered quantum mechanics in classical electromagnetic fields), the consideration of quantum field theory on a curved background has led to predictions such as black hole radiation.
More recently, the approach has been further implemented to include an algebraic version of quantum field theory in curved spacetime. Indeed, the viewpoint of local quantum physics is in particular suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. Several rigorous results concerning QFT in presence of a black hole have been obtained.
In 1979 he pioneered the modern view on the renormalization aspect of quantum field theory that considers all quantum field theories as effective field theories and changed the viewpoint of previous work (including his own in his 1967 paper) that a sensible quantum field theory must be renormalizable. This approach allowed the development of effective theory of quantum gravity, low energy QCD, heavy quark effective field theory and other developments, and it is a topic of considerable interest in current research.
Much of the difficulty in meshing these theories at all energy scales comes from the different assumptions that these theories make on how the universe works. General relativity models gravity as curvature of spacetime: in the slogan of John Archibald Wheeler, "Spacetime tells matter how to move; matter tells spacetime how to curve." On the other hand, quantum field theory is typically formulated in the "flat" spacetime used in special relativity. No theory has yet proven successful in describing the general situation where the dynamics of matter, modeled with quantum mechanics, affect the curvature of spacetime. If one attempts to treat gravity as simply another quantum field, the resulting theory is not renormalizable. Even in the simpler case where the curvature of spacetime is fixed "a priori," developing quantum field theory becomes more mathematically challenging, and many ideas physicists use in quantum field theory on flat spacetime are no longer applicable.
Looking at the development of topological quantum field theory we should consider that it has many applications to Seiberg–Witten gauge theory, topological string theory, the relationship between knot theory and quantum theory, and quantum knot invariants. Furthermore, it has provided objects of great interest to both mathematics and physics. Also of important recent interest are non-local operators in TQFT. (). If string theory is viewed as the fundamental, then non-local TQFTs can be viewed as non-physical models that provide a computationally efficient approximation to local string theory.
Since the end of the eighties, the local quantum field theory approach due to Rudolf Haag and Daniel Kastler has been implemented in order to include an algebraic version of quantum field theory in curved spacetime. Indeed, the viewpoint of local quantum physics is suitable to generalize the renormalization procedure to the theory of quantum fields developed on curved backgrounds. Several rigorous results concerning QFT in the presence of a black hole have been obtained. In particular the algebraic approach allows one to deal with the problems, above mentioned, arising from the absence of a preferred reference vacuum state, the absence of a natural notion of particle and the appearance of unitarily inequivalent representations of the algebra of observables. (See these lecture notes 
Early attempts to merge quantum mechanics with special relativity involved the replacement of the Schrödinger equation with a covariant equation such as the Klein–Gordon equation or the Dirac equation. While these theories were successful in explaining many experimental results, they had certain unsatisfactory qualities stemming from their neglect of the relativistic creation and annihilation of particles. A fully relativistic quantum theory required the development of quantum field theory, which applies quantization to a field (rather than a fixed set of particles). The first complete quantum field theory, quantum electrodynamics, provides a fully quantum description of the electromagnetic interaction. The full apparatus of quantum field theory is often unnecessary for describing electrodynamic systems. A simpler approach, one that has been employed since the inception of quantum mechanics, is to treat charged particles as quantum mechanical objects being acted on by a classical electromagnetic field. For example, the elementary quantum model of the hydrogen atom describes the electric field of the hydrogen atom using a classical formula_2 Coulomb potential. This "semi-classical" approach fails if quantum fluctuations in the electromagnetic field play an important role, such as in the emission of photons by charged particles.
Quantum field theories for the strong nuclear force and the weak nuclear force have also been developed. The quantum field theory of the strong nuclear force is called quantum chromodynamics, and describes the interactions of subnuclear particles such as quarks and gluons. The weak nuclear force and the electromagnetic force were unified, in their quantized forms, into a single quantum field theory (known as electroweak theory), by the physicists Abdus Salam, Sheldon Glashow and Steven Weinberg. These three men shared the Nobel Prize in Physics in 1979 for this work.
Källén's research focused on quantum field theory and elementary particle physics. His developments included the so-called Källén–Lehmann representation of correlation functions in quantum field theory, and he made contributions to quantum electrodynamics, especially in renormalizing. He also worked with the axiomatic formulation of quantum field theory, which led to contributions to the theory of functions of several complex variables. He collaborated on the Pauli–Källén equation. The Källén function is named after him.
The effort to put physical theories on a mathematically rigorous footing has inspired many mathematical developments. For example, the development of quantum mechanics and some aspects of functional analysis parallel each other in many ways. The mathematical study of quantum mechanics, quantum field theory, and quantum statistical mechanics has motivated results in operator algebras. The attempt to construct a rigorous quantum field theory has also brought about progress in fields such as representation theory. Use of geometry and topology plays an important role in string theory.
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 light and electrons, culminating in the first quantum field theory — quantum electrodynamics. 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. A second major barrier came with QFT's apparent inability to describe the weak and strong interactions, to the point where some theorists called for the abandonment of the field theoretic approach. The development of gauge theory and the completion of the Standard Model in the 1970s led to a renaissance of quantum field theory.
Rivasseau's research deals with constructive quantum field theory and renormalization theory with applications to many-body theory, such as quantum interacting fermions in solid state physics. Since 2004 he has studied quantum field theories on noncommutative space-time,
then group field theory. Since 2011 he develops the tensor track approach to quantum gravity 
based on random tensors
(higher-dimensional generalizations of random matrices).
Later the electromagnetic field was also quantized, and even the particles themselves became represented through quantized fields, resulting in the development of quantum electrodynamics (QED) and quantum field theory in general. Thus, by convention, the original form of particle quantum mechanics is denoted first quantization, while quantum field theory is formulated in the language of second quantization.