PlanetPhysics/Categorical Quantum LM Algebraic Logic 2

From testwiki
Jump to navigation Jump to search

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-- U(1) and SU(3)-- group symmetries. This obviates the need for `more fundamental' , or [[../ExtendedQuantumSymmetries/|extended quantum symmetries]], such as those afforded by either larger groups such as SU(3)×SU(2)×U(1) 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]], Glc 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]].

All Sources

[2] [3] [4] [1] [5] [6] [7] [7] [8] [9] [10] [11]

References

  1. ↑ 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).
  2. ↑ A. Abragam and B. Bleaney.: Electron Paramagnetic Resonance of Transition Ions. Clarendon Press: Oxford, (1970).
  3. ↑ E. M. Alfsen and F. W. Schultz: \emph{Geometry of State Spaces of Operator Algebras}, Birkh\"auser, Boston--Basel--Berlin (2003).
  4. ↑ D.N. Yetter., TQFT's from homotopy 2-types. J. Knot Theor . 2 : 113--123(1993).
  5. ↑ A. Weinstein : Groupoids: unifying internal and external symmetry, Notices of the Amer. Math. Soc. 43 (7): 744--752 (1996).
  6. ↑ J. Wess and J. Bagger: Supersymmetry and Supergravity , Princeton University Press, (1983).
  7. ↑ 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
  8. ↑ S. Wickramasekara and A. Bohm: Symmetry representations in the rigged Hilbert space formulation of quantum mechanics, J. Phys. A 35 (3): 807-829 (2002).
  9. ↑ Wightman, A. S., 1956, Quantum Field Theory in Terms of Vacuum Expectation Values, Physical Review, 101 : 860--866.
  10. ↑ Wightman, A.S. and Garding, L., 1964, Fields as Operator--Valued Distributions in Relativistic Quantum Theory, Arkiv f\"ur Fysik, 28: 129--184.
  11. ↑ S. L. Woronowicz : Twisted SU(2) group : An example of a non--commutative differential calculus, RIMS, Kyoto University 23 (1987), 613--665.

Template:CourseCat

Retrieved from "https://en.wikiversity.beta.math.wmflabs.org/w/index.php?title=PlanetPhysics/Categorical_Quantum_LM_Algebraic_Logic_2&oldid=2147"