Wightman axiomatic approach in noncommutative field theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 403-416 Cet article a éte moissonné depuis la source Math-Net.Ru

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The axiomatic approach based on Wightman functions is developed in noncommutative field theory. We prove that the main results of the axiomatic approach remain valid if the noncommutativity affects only the spatial variables.
Keywords: noncommutativity, quantum field theory, axiomatic approach, Wightman functions, local commutativity, spectrality, $CPT$ theorem.
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Yu. S. Vernov; M. N. Mnatsakanova. Wightman axiomatic approach in noncommutative field theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 142 (2005) no. 2, pp. 403-416. http://geodesic.mathdoc.fr/item/TMF_2005_142_2_a15/

[1] R. Striter, A. Vaitman, $PCT$, spin i statistika i vse takoe, Nauka, M., 1966

[2] R. Iost, Obschaya teoriya kvantovannykh polei, Mir, M., 1967 | MR

[3] N. N. Bogolyubov, A. A. Logunov, I. T. Todorov, Osnovy aksiomaticheskogo podkhoda v kvantovoi teorii polya, Nauka, M., 1969 | MR

[4] R. Haag, Local Quantum Physics, Springer, Berlin, 1996 | MR

[5] G. Morchio, F. Strocchi, Ann. Inst. H. Poincaré A, 33 (1980), 251 | MR

[6] F. Strocchi, Selected Topics on the General properties of Quantum Field Theory, World Scientific, Singapore, 1993 | MR | Zbl

[7] A. A. Logunov, M. A. Mestvirishvili, O. A. Khrustalev, EChAYa, 3 (1972), 3

[8] H. S. Snyder, Phys. Rev., 71 (1947), 38 | DOI | MR | Zbl

[9] A. Connes, Noncommutative Geometry, Acad. Press, New York, 1994 | MR | Zbl

[10] S. Doplicher, K. Fredenhagen, J. E. Roberts, Phys. Lett. B, 331 (1994), 39 ; Commun. Math. Phys., 172 (1995), 187 | DOI | MR | DOI | MR | Zbl

[11] N. Seiberg, E. Witten, JHEP, 9909 (1999), 32 ; E-print hep-th/9908142 | DOI | MR

[12] M. R. Douglas, N. A. Nekrasov, Rev. Mod. Phys., 73 (2001), 977 ; E-print hep-th/0106048 | DOI | MR | Zbl

[13] R. J. Szabo, Phys. Rep., 378 (2003), 207 ; E-print hep-th/0109162 | DOI | MR | Zbl

[14] J. Gomis, T. Mehen, Nucl. Phys. B, 591 (2000), 265 ; E-print hep-th/0005129 | DOI | MR | Zbl

[15] N. Seiberg, L. Susskind, N. Toumbas, JHEP, 0006 (2000), 044 ; ; L. Álvarez-Gaumé, J. L. F. Barbon, Int. J. Mod. Phys. A, 16 (2001), 1123 ; E-print hep-th/0005015E-print hep-th/0006209 | DOI | MR | DOI | MR | Zbl

[16] M. Chaichian, K. Nishijima, A. Tureanu, Phys. Lett. B, 568 (2003), 146 ; E-print hep-th/0209008 | DOI | MR | Zbl

[17] O. Aharony, J. Gomis, T. Mehen, JHEP, 0009 (2000), 023 ; E-print hep-th/0006236 | DOI | MR

[18] Yi Liao, K. Sibold, Phys. Lett. B, 549 (2002), 352 ; E-print hep-th/0209221 | DOI | MR | Zbl

[19] M. Chaichian, M. Mnatsakanova, A. Tureanu, Yu. Vernov, Nucl. Phys. B, 673 (2003), 476 ; E-print hep-th/0306158 | DOI | MR | Zbl

[20] Yu. S. Vernov, M. N. Mnatsakanova, TMF, 139 (2004), 3 | DOI | MR | Zbl

[21] M. Chaichian, A. Tureanu, Jost–Lehmann–Dyson representation and Froissart–Martin bound in quantum field theory on noncommutative space-time, E-print hep-th/0403032

[22] Yu. S. Vernov, M. M. Mnatsakanova, TMF, 142 (2005), 388 ; E-print hep-th/0403033 | DOI | MR | Zbl

[23] J. Mund, B. Schroer, J. Yngvason, Phys. Lett. B, 596 (2004), 156 ; E-print math-ph/0402043 | DOI | MR | Zbl

[24] S. Doplicher, “Spacetime and fields, a quantum texture”, New Developments in Fundamental interaction Theories, 37th Karpacz Winter School of Theoretical Physics (Karpacz, Poland, Febr. 6–15, 2001), AIP Conf. Proc., 589, eds. J. Lukierski, J. Rembielinski, AIP, Melville, NY, 2001, 204 ; E-print hep-th/0105251 | DOI

[25] R. Brunetti, K. Fredenhagen, R. Verch, Commun. Math. Phys., 237 (2003), 31 ; E-print math-ph/0112041 | DOI | MR | Zbl

[26] L. Álvarez-Gaumé, M. A. Vázquez-Mozo, Nucl. Phys. B, 668 (2003), 293 ; E-print hep-th/0305093 | DOI | MR | Zbl

[27] M. Chaichian, M. N. Mnatsakanova, K. Nishijima, A. Tureanu, Yu. S. Vernov, Towards an axiomatic formulation of noncommutative quantum field theory, E-print hep-th/0402212 | MR

[28] L.Álvarez-Gaumé, J. L. F. Barbon, R. Zwicky, JHEP, 0105 (2001), 057 ; E-print hep-th/0103069 | DOI | MR

[29] D. H. T. Franco, On the Borchers class of a non-commutative field, E-print hep-th/0404029 | MR

[30] O. Shteinman, Metod vozmuschenii v aksiomaticheskoi teorii polya, Mir, M., 1974 | MR

[31] V. S. Vladimirov, Metody teorii funktsii mnogikh kompleksnykh peremennykh, Nauka, M., 1964 | MR