PlanetPhysics/Categorical Quantum LM Algebraic Logic 2
This topic links the general framework of [[../SpaceTimeQuantizationInQuantumGravityTheories/|quantum field theories]] to [[../TrivialGroupoid/|group]] symmetries and other relevant mathematical [[../PreciseIdea/|concepts]] utilized to represent [[../CosmologicalConstant/|quantum fields]] and their fundamental properties.
Fundamental, mathematical concepts in quantum field theory
Quantum field theory (QFT) is the general framework for describing the physics of relativistic quantum [[../GenericityInOpenSystems/|systems]], such as, notably, accelerated elementary [[../Particle/|particles]].
[[../QED/|Quantum electrodynamics]] (QED) , and QCD or quantum chromodynamics are only two distinct theories among several quantum field theories, as their fundamental [[../CategoricalGroupRepresentation/|representations]] correspond, respectively, to very different-- and -- group symmetries. This obviates the need for `more fundamental' , or [[../ExtendedQuantumSymmetries/|extended quantum symmetries]], such as those afforded by either larger groups such as or spontaneously broken, special symmetries of a less restrictive kind present in `[[../QuantumGroupoids/|quantum groupoids]]' as for example in [[../WeakHopfAlgebra/|weak Hopf algebra]] representations, or in [[../LocallyCompactGroupoid/|locally compact groupoid]], unitary representations, and so on, to the higher dimensional (quantum) symmetries of [[../LongRangeCoupling/|quantum double groupoids]], quantum [[../GeneralizedSuperalgebras/|double algebroids]], [[../QuantumCategories/|quantum categories]],quantum [[../SuperdiagramsAsHeterofunctors/|supercategories]] and/or quantum [[../HamiltonianAlgebroid3/|supersymmetry superalgebras]] (or graded `[[../BilinearMap/|Lie' algebras]]), see, for example, their full development in a recent QFT textbook [1] that lead to [[../GeneralizedSuperalgebras/|superalgebroids]] in [[../LQG2/|quantum gravity]] or [[../ExtendedQuantumSymmetries/|QCD]].
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References
- ↑ 1.0 1.1 S. Weinberg.: The Quantum Theory of Fields . Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3, (1995--2000).
- ↑ A. Abragam and B. Bleaney.: Electron Paramagnetic Resonance of Transition Ions. Clarendon Press: Oxford, (1970).
- ↑ E. M. Alfsen and F. W. Schultz: \emph{Geometry of State Spaces of Operator Algebras}, Birkh\"auser, Boston--Basel--Berlin (2003).
- ↑ D.N. Yetter., TQFT's from homotopy 2-types. J. Knot Theor . 2 : 113--123(1993).
- ↑ A. Weinstein : Groupoids: unifying internal and external symmetry, Notices of the Amer. Math. Soc. 43 (7): 744--752 (1996).
- ↑ J. Wess and J. Bagger: Supersymmetry and Supergravity , Princeton University Press, (1983).
- ↑ 7.0 7.1
J. Westman: Harmonic analysis on groupoids, Pacific J. Math. 27 : 621-632. (1968).
Cite error: Invalid
<ref>tag; name "WJ1" defined multiple times with different content - ↑ S. Wickramasekara and A. Bohm: Symmetry representations in the rigged Hilbert space formulation of quantum mechanics, J. Phys. A 35 (3): 807-829 (2002).
- ↑ Wightman, A. S., 1956, Quantum Field Theory in Terms of Vacuum Expectation Values, Physical Review, 101 : 860--866.
- ↑ Wightman, A.S. and Garding, L., 1964, Fields as Operator--Valued Distributions in Relativistic Quantum Theory, Arkiv f\"ur Fysik, 28: 129--184.
- ↑ S. L. Woronowicz : Twisted SU(2) group : An example of a non--commutative differential calculus, RIMS, Kyoto University 23 (1987), 613--665.