When was quantum field theory developed?
2078963#10
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; this procedure is now sometimes called second quantization. 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.
History of quantum field theory
25267#2
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.
Quantum field theory
20728#12
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.
Mathematical formulation of quantum mechanics
2078963#15
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.
History of quantum field theory
2078963#6
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.
History of quantum field theory
25267#12
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. With the exclusion of interactions, however, such a theory was yet incapable of making quantitative predictions about the real world.
Quantum field theory
25202#39
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 mechanics
2796131#75
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.
Introduction to quantum mechanics
1057601#3
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
Quantum field theory in curved spacetime
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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.
Quantum gravity