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quantum field theories
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(Definition)
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Q.E.D or Quantum Electrodynamics, and QCD or Quantum Chromodynamics are only two distinct theories among several Quantum Field theories, as their fundamental representations correspond, respectively, to very different-  and  - group symmetries. This
obviates the need for `more fundamental' , or 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 `quantum groupoids' as for example in weak Hopf algebra representations, or in locally compact groupoid,  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 recent QFT books [4] that lead
to superalgebroids in quantum gravity or QCD.
- 1
- A. Abragam and B. Bleaney.: Electron Paramagnetic Resonance of Transition Ions. Clarendon Press: Oxford, (1970).
- 2
- E. M. Alfsen and F. W. Schultz: Geometry of State Spaces of Operator Algebras, Birkhäuser, Boston-Basel-Berlin (2003).
- 3
- D.N. Yetter., TQFT's from homotopy 2-types. J. Knot Theor. 2: 113–123(1993).
- 4
- S. Weinberg.: The Quantum Theory of Fields. Cambridge, New York and Madrid: Cambridge University Press, Vols. 1 to 3, (1995-2000).
- 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).
- 8
- J. Westman: Harmonic analysis on groupoids, Pacific J. Math. 27: 621-632. (1968).
- 8
- J. Westman: Groupoid theory in algebra, topology and analysis., University of California at Irvine (1971).
- 9
- S. Wickramasekara and A. Bohm: Symmetry representations in the rigged Hilbert space formulation of quantum mechanics, J. Phys. A 35(3): 807-829 (2002).
- 10
- Wightman, A. S., 1956, Quantum Field Theory in Terms of Vacuum Expectation Values, Physical Review, 101: 860-866.
- 11
- Wightman, A.S. and Gårding, L., 1964, Fields as Operator-Valued Distributions in Relativistic Quantum Theory, Arkiv fur Fysik, 28: 129-184.
- 12
- S. L. Woronowicz : Twisted SU(2) group : An example of a non-commutative differential calculus, RIMS, Kyoto University 23 (1987), 613-665.
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"quantum field theories" is owned by bci1.
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See Also: quantum electrodynamics, quantum chromodynamics (QCD), algebroid structures and extended symmetries, distribution, algebraic quantum field theories (AQFT), quantization, quantum chromodynamics (QCD)
| Other names: |
quantum theories |
| Also defines: |
quantum interactions of all kinds, minus gravitational ones |
| Keywords: |
quantum fields, quantum theories, QED, QCD, Yang-Mills theories, non-Abelian gauge theories |
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Cross-references: QCD, quantum gravity, development, graded Lie algebras, superalgebras, supersymmetry, supercategories, quantum categories, double groupoids, unitary representations, locally compact groupoid, weak Hopf algebra, quantum groupoids, extended quantum symmetries, symmetries, group, representations, theories, quantum electrodynamics
There are 16 references to this entry.
This is version 23 of quantum field theories, born on 2008-07-06, modified 2008-10-17.
Object id is 10753, canonical name is QFTOrQuantumFieldTheories.
Accessed 973 times total.
Classification:
| AMS MSC: | 81T05 (Quantum theory :: Quantum field theory; related classical field theories :: Axiomatic quantum field theory; operator algebras) | | | 81T10 (Quantum theory :: Quantum field theory; related classical field theories :: Model quantum field theories) | | | 81T13 (Quantum theory :: Quantum field theory; related classical field theories :: Yang-Mills and other gauge theories) | | | 81T18 (Quantum theory :: Quantum field theory; related classical field theories :: Feynman diagrams) | | | 81T25 (Quantum theory :: Quantum field theory; related classical field theories :: Quantum field theory on lattices) | | | 81T40 (Quantum theory :: Quantum field theory; related classical field theories :: Two-dimensional field theories, conformal field theories, etc.) | | | 81T60 (Quantum theory :: Quantum field theory; related classical field theories :: Supersymmetric field theories) | | | 81T70 (Quantum theory :: Quantum field theory; related classical field theories :: Quantization in field theory; cohomological methods) | | | 81T75 (Quantum theory :: Quantum field theory; related classical field theories :: Noncommutative geometry methods) | | | 81T80 (Quantum theory :: Quantum field theory; related classical field theories :: Simulation and numerical modeling) | | | 55U99 (Algebraic topology :: Applied homological algebra and category theory :: Miscellaneous) |
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Pending Errata and Addenda
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