Abstract
Various topics in the theory and application of the geometrical approach to supermanifolds are discussed. The construction of the superspace used in supergravity over an arbitrary spacetime manifold is described. Super Lie groups and their relation to graded Lie algebras (and more general structures referred to as ‘graded Lie modules’) are discussed, with examples. Certain supermanifolds, allowed in the geometric approach (using the fine topology), but having no analogue in the algebraic approach, are discussed. Finally lattice supersymmetry, and its relation to the differential geometry of supermanifolds, is discussed.
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References
Berezin, F.A., and Lelîtes, D.A., Sov. Math. Dokl. 16, 1218 (1975).
Kostant, B., “Graded manifolds, graded Lie theory and prequantization” in Differential Geometric Methods in Mathematical Physics, proceedings of the Symposium held at Bonn, July 1975, Lecture Notes in Mathematics 570 (Springer Verlag, 1977 ).
De Witt, B.S., Austin University Preprint (1977), (to be published).
Batchelor, M., Trans Am. Math. Soc. 258, 257 (1980).
Rogers, A., Journ. Math. Phys. 21 1352 (1980).
Jadczyk, A., and Pilch, K., Comm. Math. Phys. 78, 373 (1981).
Batchelor, M., lectures in in this volume, p. 91.
Volkov, D.V., and Akulov, V.P., Phys. Lett. 46B, 109 (1973). Abdus Salam and Strathdee, J., Nuc. Phys. B76, 477 (1974).
Volkov, D.V., and Akulov, V.P., Phys. Lett. 46B, 109 (1973). Abdus Salam and Strathdee, J., Nuc. Phys. B76, 477 (1974).
Wess, J., and Zumino, B., Phys. Lett. 66B, 361 (1977).
Bonora, L., Pasti, P., and Tonin, M., Journ. Math. Phys. 23 839 (1982).
Rogers, A., “Integration on Supermanifolds”, article in this volume, p. 135.
Rogers, A., “The geometry of curved superspace and supergravity”, London University Ph.D. Thesis (1981).
Rogers, A., Journ. Math. Phys. 22 939 (1981).
Rogers, A., Journ. Math. Phys. 22 443 (1981).
Rempel, S., and Schmitt, T., Seminar. Analysis, 1981 /82, 92–131, Akad. Wiss. DDR, Berlin 1982.
Berezin, F.A., Sov. J. Nucl. Phys. 30, 605 (1979).
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Nahm, W., Nucl. Phys. B135 (1978) 149. Green, M.B., and Schwarz J.H., Phys. Lett. 109B, 444 (1982), 122B 143 (1983). Schwarz, J.H., and West, P., Phys. Lett. 126B, 301 (1983). Howe, P.S., and West P., King’s College preprint, (1983) (to be published in Nucl. Phys. B). Schwarz, J.H., 1983 Caltech preprint.
Alvarez-Gaumé, L., and Witten E., 1983 Princeton Preprint.
Dondi, P.H., and Nicolai, H., Nuov. Cim. 41A (1977) 1. Banks, T., and Windey, P., Nucl. Phys. B198 (1982), 226. Rittenberg, V. and Yankielowicz, S., CERN TH 3263 (1982). Elitzur E., Rabinovici, E., and Schwimmer, A., Phys. Lett. 119B 165 (1982).
Dondi, P.H., and Nicolai, H., Nuov. Cim. 41A (1977) 1. Banks, T., and Windey, P., Nucl. Phys. B198 (1982), 226. Rittenberg, V. and Yankielowicz, S., CERN TH 3263 (1982). Elitzur E., Rabinovici, E., and Schwimmer, A., Phys. Lett. 119B 165 (1982).
Dondi, P.H., and Nicolai, H., Nuov. Cim. 41A (1977) 1. Banks, T., and Windey, P., Nucl. Phys. B198 (1982), 226. Rittenberg, V. and Yankielowicz, S., CERN TH 3263 (1982). Elitzur E., Rabinovici, E., and Schwimmer, A., Phys. Lett. 119B 165 (1982).
Dondi, P.H., and Nicolai, H., Nuov. Cim. 41A (1977) 1. Banks, T., and Windey, P., Nucl. Phys. B198 (1982), 226. Rittenberg, V. and Yankielowicz, S., CERN TH 3263 (1982). Elitzur E., Rabinovici, E., and Schwimmer, A., Phys. Lett. 119B 165 (1982).
Kostelecký, V.A., and Rabin, J.M., Los Alamos preprint LA-UR-83-1373 (1983).
Scott, D., Edinburgh University Preprint 83 /255 (1983).
Becher, P., and Joos, H., Desy Preprint 82 - 031 (1982).
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Rogers, A. (1984). Aspects of the Geometrical Approach to Supermanifolds. In: Seifert, HJ., Clarke, C.J.S., Rosenblum, A. (eds) Mathematical Aspects of Superspace. NATO ASI Series, vol 132. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6446-4_5
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DOI: https://doi.org/10.1007/978-94-009-6446-4_5
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