Abstract
This is a pedagogical digest of results reported in [Curtright, Fairlie, & Zachos 1997], and an explicit implementation of Euler’s construction for the solution of the Poisson Bracket dual Nahm equation. But it does not cover 9 and 10-dimensional systems, and subsequent progress on them [Fairlie 1997]. Cubic interactions are considered in 3 and 7 space dimensions, respectively, for bosonic membranes in Poisson Bracket form. Their symmetries and vacuum configurations are explored. Their associated first order equations are transformed to Nahm’s equations, and are hence seen to be integrable, for the 3-dimensional case, by virtue of the explicit Lax pair provided. Most constructions introduced also apply to matrix commutator or Moyal Bracket analogs.
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Banks, T., Fischler, W., Shenker, S., and Susskind, L. (1997): Phys Rev D55 5112
Biran, B., Floratos, E., and Savvidi, G. (1987): Phys Lett B198 329
Collins, P., and Tucker, R. (1976): Nucl Phys B112 150
Corrigan, E., Devchand, C., Fairlie, D., and Nuyts, J. (1982): Nucl Phys B214 452
Curtright, T., Fairlie, D., and Zachos, C. (1997): Phys Lett B405 37
Curtright, T. and McCarty, T. (1989): ICTP'89 talk (unpublished), (http://phyvax.ir.miami.edu:8001/curtright/ictp89.html); and the latter's University of Florida Thesis (unpublished)
Curtright, T., and Zachos, C. (1995): in PASCOS'94, K. C. Wali (ed), (World Scientific), pp 381–390, (hep-th/9407044)
Dündarer, R., Gürsey, F., and Tze, C-H. (1984): J Math Phys 25 1496
Ericksen, J. (1960): Appendices 32, 34, & 35 in Vol. III/1 of the Encyclopedia of Physics (Handbuch der Physik), S. Flügge (ed), (Springer, Berlin) pp 822–829
Fairlie, D. (1997): hep-th/9707190
Fairlie, D., Fletcher, P., and Zachos, C. (1989): Phys Lett B218 203
D. Fairlie and C. Zachos, Phys Lett B224 (1989) 101
Fairlie, D., Fletcher, P., and Zachos, C. (1990): J Math Phys 31 1088
Fairlie, D., and Strachan, I. (1996): Physica D90 1
Floratos, E., (1989): Phys Lett B228 335
Floratos, E., Iliopoulos, J., and Tiktopoulos, G. (1989): Phys Lett B217 285
also see B. de Wit, J. Hoppe, and H. Nicolai, Nucl Phys B305 [FS23] (1988) 545
J. Hoppe, Int J Mod Phys A4 (1989) 5235
E. Bergshoeff, E. Sezgin, Y. Tanii, and P. Townsend, Ann Phys 199 (1990) 340
Floratos, E., and Leontaris, G. (1989): Phys Lett B223 153
Hitchin, M. (1983): Comm Math Phys 89 145
Hoppe, J. (1982): M.I.T. Ph.D. Thesis; also in Elem Part Res J (Kyoto) 83 no.3 (1989/90)
Hoppe, J. (1990): Phys Lett B250 44
Kim, N., and Rey, S-J. (1997): hep-th/9701139
Matinyan, S., Savvidy, G., and Ter-Arutunian Savvidy, N. (1981): Sov Phys JETP 53 421; JETP Lett 34 (1981) 590
S. Matinyan, E. Prokhorenko, and G. Savvidy, Nucl Phys B298 (1988) 414
Moyal, J. (1949): Proc Camb Phil Soc 45 99; further see
J. Vey, Comment Math Helvetici 50 (1975) 412
T. Jordan and E. Sudarshan, Rev Mod Phys 33 (1961) 515
D. Fairlie, Proc Camb Phil Soc 60 (1964) 581
D. Fairlie and C. Manogue, J Phys A24 (1991) 3807
Nahm, W. (1983): in Group Theoretical Methods in Physics: XIth International Colloquium, Istanbul, 1982, M. Serdaroğlu and E. Ínönü (eds), (Springer Lecture Notes in Physics 180, Berlin) pp 456–466
Plebański, J., Przanowski, M., and García-Compeán, H. (1996): Mod Phys Lett A11 663
Schild, A. (1977): Phys Rev D16 1722
aso see T. Eguchi, Phys Rev Lett 44 (1980) 126
Ward, R. (1990): Phys Lett B234 81
Zaikov, R. (1991): Phys Lett B266 303
Zakharov, V., and Mikhailov, A. (1978): Sov Phys JETP 47 1017
T. Curtright and C. Zachos, Phys Rev D49 (1994) 5408
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Zachos, C., Fairlie, D., Curtright, T. (1998). Matrix membranes and integrability. In: Aratyn, H., Imbo, T.D., Keung, WY., Sukhatme, U. (eds) Supersymmetry and Integrable Models. Lecture Notes in Physics, vol 502. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0105319
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DOI: https://doi.org/10.1007/BFb0105319
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