quantum field theories (QFT) delCategoricalQuantumLMAlgebraicLogic22008-12-14 22:33:502009-03-05 11:27:58Topicoverview of the content of PlanetPhysicsquantum group symmetriesQFTquantum fieldsquantum theoriesQEDQCDYang-Mills theoriesnon-Abelian gauge theories% this is the default PlanetPhysics preamble. as your knowledge
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% define commands hereThis topic links the general framework of quantum field theories to group symmetries
and other relevant mathematical concepts utilized to represent quantum fields
and their fundamental properties.
\subsection{Fundamental, mathematical concepts in quantum field theory }
\emph{Quantum field theory (QFT)} is the general framework for describing the physics of relativistic quantum systems, such as, notably, accelerated elementary particles.
Quantum electrodynamics \emph{(QED)}, and \PMlinkname{QCD or quantum chromodynamics}{QCDorQuantumChromodynamics} are only two distinct theories among several quantum field theories, as their fundamental representations correspond, respectively, to very different-- $U(1)$ and $SU(3)$-- group symmetries. This obviates the need for `more fundamental' , or extended quantum symmetries, such as those afforded by either larger groups such as
$SU(3) \times SU(2) \times U(1)$ or spontaneously broken, special symmetries of a less restrictive kind present in `quantum groupoids' as for example in weak Hopf algebra representations, or in locally compact groupoid, $G_{lc}$ unitary representations, and so on, to the higher dimensional (quantum) symmetries of quantum double groupoids, quantum double algebroids, quantum categories,quantum supercategories and/or quantum supersymmetry superalgebras (or graded `Lie' algebras), see, for example, their full development in a recent QFT textbook \cite{Weinberg2003} that lead to superalgebroids in quantum gravity or QCD.
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