On the quantum mechanics of supermembranes. Reprints. (English) Zbl 1156.81457

Duff, M.J. (ed.), The world in eleven dimensions: supergravity, supermembranes and M-theory. Bristol: IoP, Institute of Physics Publishing (ISBN 0-7503-0672-6/pbk; 0-7503-0671-8/hbk). Stud. High Energy Phys. Cosmol. Gravit., 73-109 (1999).
Summary: We study the quantum-mechanical properties of a supermembrane and examine the nature of its ground state. A supersymmetric gauge theory of area-preserving transformations provides a convenient framework for this study. The supermembrane can be viewed as a limiting case of a class of models in supersymmetric quantum mechanics. Its mass does not depend on the zero modes and vanishes only if the wave function is a singlet under supersymmetry transformations of the nonzero modes. We exhibit the complexity of the supermembrane ground state and examine various truncations of these models. None of these truncations has massless states.
For the entire collection see [Zbl 0999.00513].


81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
83E50 Supergravity
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[1] Bergshoeff, E.; Sezgin, E.; Townsend, P. K., Ann. of Phys., 185, 330 (1988)
[2] Siegel, W., Class. Quantum Grav., 2, L95-L97 (1985)
[3] Green, M. B.; Schwarz, J. H., Nucl. Phys., B243, 285 (1984)
[4] Hughes, J.; Liu, J.; Polchinsky, J., Phys. Lett., 180B, 370 (1986)
[5] Henneaux, M.; Mezincescu, L., Phys. Lett., 152B, 340 (1985)
[6] Duff, M. J.; Inami, T.; Pope, C. N.; Sezgin, E.; Stelle, K. S., Nucl. Phys., B297, 515 (1988)
[8] Brink, L.; Nielsen, H. B., Phys. Lett., 45B, 332 (1973)
[9] Kikkawa, K.; Yamasaki, M., Progr. Theor. Phys., 76, 1379 (1986)
[10] Bars, I., USC-87/HEP06 (1987), preprint
[12] Hoppe, J., (Longhi, G.; Lusanna, L., Proc. Int. Workshop on Constraint’s theory and relativistic dynamics (1987), World Scientific)
[13] Nicolai, H., J. Phys., A10, 2143 (1977)
[14] De Crombrugghe, M.; Rittenberg, V., Ann. of Phys., 151, 99 (1983)
[15] Claudson, M.; Halpern, M. B., Nucl. Phys., B250, 689 (1985)
[16] Bergshoeff, E.; Duff, M. J.; Pope, C. N.; Sezgin, E., Phys. Lett., 199B, 69 (1987)
[19] Bergshoeff, E.; Sezgin, E.; Tanii, Y., Nucl. Phys., B298, 187 (1988)
[20] Dirac, P. A.M., Lectures on quantum mechanics, Belfer Grad. School of Science Monograph Series 2 (1964), New York · Zbl 0141.44603
[21] Arnold, V. I., Mathematical methods of classical mechanics (1978), Springer · Zbl 0386.70001
[22] Messiah, A., (Quantum mechanics, vols. I and II (1966), North-Holland)
[23] Judd, Operator techniques in atomic spectroscopy (1963), McGraw-Hill
[25] Floratos, E.; Iliopoulos, J., Phys. Lett., 201B, 237 (1988)
[26] Garreis, R., Karlsruhe Ph.D. Thesis (1988)
[27] Brézin, E.; Itzykson, C.; Parisi, G.; Zuber, J.-B., Commun. Math. Phys., 59, 35 (1978)
[28] Green, M. B.; Schwarz, J. H.; Witten, E., (Superstring theory, vol. 2 (1987), Cambridge Univ. Press)
[29] Günaydin, M.; Gürsey, F., J. Math. Phys., 14, 1651 (1973)
[30] de Wit, B.; Nicolai, H., Nucl. Phys., B231, 506 (1984)
[31] Courant, R.; Hilbert, D., (Methods of mathematical physics, vol. 2 (1962), Interscience Publ) · Zbl 0729.00007
[32] Slansky, R., Phys. Reports, 79, 1 (1981)
[33] Smilga, A. V., Nucl. Phys., B266, 45 (1986)
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