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Twisted second quantization. (English) Zbl 0707.47039
Summary: A formalism of a second quantization procedure based upon the twisted SU(N) group is constructed and the related twisted canonical commutation relations (TCCR) are investigated. In a particular case, these relations reduce to classical CCR. Irreducible representations of TCCR are described. The Stone-von Neumann uniqueness theorem does not hold for the general TCCR.

##### MSC:
 47N50 Applications of operator theory in the physical sciences 81S05 Commutation relations and statistics as related to quantum mechanics (general)
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##### References:
 [1] Barut, A.O.; Ra̧czka, R., Theory of group representations and applications, (1977), PWN-Polish Scientific Publishers · Zbl 0132.27901 [2] Borchers, H.J.; Yngvason, J., Commun. math. phys., 42, 231-252, (1975) [3] Drinfeld, V.S., Quantum groups, (1986), will appear in Proceedings ICM [4] Enock, M.; Schwartz, J.M., Bull. soc. math. France, suplément mémoire, 44, 1-44, (1975) [5] Flato, M.; Simon, J.; Shellmann, H.; Sternheimer, D., Annales scient. ecole normale sup. 4^{e} serie 5, 423-434, (1972) [6] Pusz, W.: Twisted canonical anticommutation relations (to appear in Reports on Mathematical Physics). · Zbl 0752.17035 [7] Powers, R., Commun. math. phys., 21, 85-124, (1971) [8] Schwartz, J.M., J. funct. anal., 34, 370-406, (1979) [9] Slowikowski, W., Commutative Wick algebras I. the bargman, weiner and Fock algebras, () · Zbl 0391.28010 [10] Woronowicz, S.L., Commun. math. phys., 111, 613-665, (1987) [11] Woronowicz, S.L., Tannaka-Krein duality for compact matrix pseudogroups. twisted SU (N) groups, Invent. math., 93, 35-76, (1988) · Zbl 0664.58044
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