quantum field theories (QFT)
This 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.
Quantum field theory (QFT) is the general framework for describing the physics of relativistic quantum systems, such as, notably, accelerated elementary particles.
Quantum electrodynamics
(QED), 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 a recent QFT textbook [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 Garding, L., 1964, Fields as Operator-Valued Distributions in Relativistic Quantum Theory, Arkiv für 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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