zbMATH — the first resource for mathematics

Twisted canonical anticommutation relations. (English) Zbl 0752.17035
Author’s summary: “Twisted canonical anticommutation relations (TCAR) connected with a formalism of a second quantization procedure based upon the twisted $$SU(N)$$ group are described. Irreducible representations of TCAR are investigated and a uniqueness theorem is proved”.
Reviewer: G.Arca (Cagliari)

MSC:
 17B81 Applications of Lie (super)algebras to physics, etc. 81R50 Quantum groups and related algebraic methods applied to problems in quantum theory 46N50 Applications of functional analysis in quantum physics 46L85 Noncommutative topology 46L87 Noncommutative differential geometry 81S05 Commutation relations and statistics as related to quantum mechanics (general)
Full Text:
References:
 [1] Barut, A.O.; Raczka, R., Theory of group representations and applications, (1977), PWN Warsaw · Zbl 0132.27901 [2] Manin, Yu.I., Some remarks on Koszul algebras and quantum groups, Ann. inst. Fourier, 37, 4, 191, (1987) · Zbl 0625.58040 [3] Pusz, W.; Woronowicz, S.L., Twisted second quantization, Reports on math. phys., 27, 231, (1989) · Zbl 0707.47039 [4] Schweber, S.S., An introduction to relativistic quantum field theory, (1961), Row, Peterson and Co Evanstone, Ill., Elmsford, N.Y · Zbl 0111.43102 [5] Woronowicz, S.L., Compact matrix pseudogroups, Commun. math. phys., 111, 613, (1987) · Zbl 0627.58034 [6] Woronowicz, S.L., Tannaka – krein duality for compact matrix pseudogroups. twisted SU(N) groups, Invent. math., 93, 35, (1988) · Zbl 0664.58044 [7] Woronowicz, S.L., Differential calculus on compact matrix pseudogroups (quantum groups), Commun. math. phys., 122, 125, (1989) · Zbl 0751.58042
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.