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Quantum Field Theory: Particles
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Quantum Field Theory (QFT) is the general framework for the description of the physics of relativistic quantum systems, notably of elementary particles. It is the synthesis of Quantum Theory and Special Relativity, supplemented by the principle of Locality in space and time, and by the Spectral Condition in energy and momentum. Algebraic QFT (AQFT) emphasizes the role of algebraic relations among observables which determine, rather than quantum fields proper, a physical system.
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"Quantum field theory (QFT) is the application of quantum mechanics to fields. It provides a theoretical framework, widely used in particle physics and condensed matter physics, in which to formulate consistent quantum theories of many-particle systems, especially in situations where particles may be created and destroyed. Non-relativistic quantum field theories are needed in condensed matter physics— for example in the BCS theory of superconductivity. Relativistic quantum field theories are indispensable in particle physics (see the standard model), although they are known to arise as effective field theories in condensed matter physics." 01-06
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Its first achievement, namely the quantization of the electromagnetic field is “still the paradigmatic example of a successful quantum field theory” Weinberg 1995. Ordinary QM cannot give an account of photons which constitute the paradigmatic case of relativistic ‘particles’. Since photons have the rest mass zero, and correspondingly travel in the vacuum at the velocity, naturally, of light c it is ruled out that a non-relativistic theory such as ordinary QM could give even an approximate description. Photons are implicitly contained in the emission and absorption processes which have to be postulated, for instance, when one of an atom's electrons makes a transition from a higher to a lower energy level or vice versa. However, only the formalism of QFT contains an explicit description of photons. Looking back one would say that most topics in the early development of quantum theory (1900–1927) were related with the interaction of radiation and matter and should be treated by quantum field theoretical methods.
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Quantum field theory is an extension of quantum mechanics from point particles to fields, such as the electromagnetic field. Development of a new theory was needed because ordinary quantum mechanics cannot describe creation or annihilation of elementary particles and is incompatible with Einstein's theory of special relativity.
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Despite its early successes, quantum field theory was plagued by several serious theoretical difficulties. Many seemingly-innocuous physical quantities, such as the energy shift of electron states due to the presence of the electromagnetic field, gave infinity — a nonsensical result — when computed using quantum field theory. This "divergence problem" was solved during the 1940s by Bethe, Tomonaga, Schwinger, Feynman, and Dyson, through the procedure known as renormalization. This phase of development culminated with the construction of the modern theory of quantum electrodynamics (QED). Beginning in the 1950s with the work of Yang and Mills, QED was generalized to a class of quantum field theories known as gauge theories. The 1960s and 1970s saw the formulation of a gauge theory now known as the Standard Model of particle physics, which describes all known elementary particles and the interactions between them.
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(QED), quantum field theory that describes the properties of electromagnetic radiation and its interaction with electrically charged matter in the framework of quantum theory. QED deals with processes involving the creation of elementary particles from electromagnetic energy, and with the reverse processes in which a particle and its antiparticle annihilate each other and produce energy. The fundamental equations of QED apply to the emission and absorption of light by atoms and the basic interactions of light with electrons and other elementary particles. Charged particles interact by emitting and absorbing photons, the particles of light that transmit electromagnetic forces. For this reason, QED is ... known as the quantum theory of light.
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