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.
0.1 Fundamental, mathematical concepts in quantum field theory
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 (http://planetmath.org/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 $U(1)\times SU(2)\times SU(3)$ 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 [4] that lead to superalgebroids in quantum gravity or QCD.
References
- 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).
- 7 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.
Title | quantum field theories (QFT) |
Canonical name | QuantumFieldTheoriesQFT |
Date of creation | 2013-03-22 18:10:52 |
Last modified on | 2013-03-22 18:10:52 |
Owner | bci1 (20947) |
Last modified by | bci1 (20947) |
Numerical id | 35 |
Author | bci1 (20947) |
Entry type | Topic |
Classification | msc 55U99 |
Classification | msc 81T80 |
Classification | msc 81T75 |
Classification | msc 81T70 |
Classification | msc 81T60 |
Classification | msc 81T40 |
Classification | msc 81T25 |
Classification | msc 81T18 |
Classification | msc 81T13 |
Classification | msc 81T10 |
Classification | msc 81T05 |
Synonym | quantum theories |
Related topic | QEDInTheoreticalAndMathematicalPhysics |
Related topic | QuantumChromodynamicsQCD |
Related topic | Algebroids |
Related topic | Distribution4 |
Related topic | AlgebraicQuantumFieldTheoriesAQFT |
Related topic | Quantization |
Related topic | QuantumChromodynamicsQCD |
Defines | quantum interactions of all kinds |
Defines | minus gravitational ones |