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The group structure of supergravity. (English) Zbl 0588.53066

The authors develop a geometric theory of partial differential equations and use it to define a group manifold structure. This is then used to formulate a theory of supergravity which has a direct interpretation as a fully covariant gauge theory. Previous formulations of supergravity do not seem to have such an interpretation. The authors illustrate their approach by recasting supergravity in 5, 6 and 11 dimensions in their formulation.
Reviewer: C.S.Sharma

MSC:

53C80 Applications of global differential geometry to the sciences
35A30 Geometric theory, characteristics, transformations in context of PDEs
83E50 Supergravity
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References:

[1] Y. Ne’eman and T. Regge , Riv. Nuovo Cimento , t. 1 , n^\circ 5 , 1978 . MR 507169
[2] A. d’Adda , R. d’Auria , P. Fre’ and T. Regge , Riv. Nuovo Cimento , t. 2 , n^\circ 6 , 1980 .
[3] R. d’Auria , P. Fre’ and T. Regge , Riv. Nuovo Cimento , t. 3 , n^\circ 12 , 1980 .
[4] R. Kerner , Comm. Math. Phys. , t. 91 , 1983 , p. 213 . Article | MR 723548 | Zbl 0536.53069 · Zbl 0536.53069
[5] R. Kerner and E.M. da Silva Maia , J. Math. Phys. , t. 24 , 1983 , p. 361 . MR 692314 | Zbl 0511.58019 · Zbl 0511.58019
[6] P. Van Nieuwenhuizen , Gen. Rel. Grav. , t. 10 , n^\circ 3 , 1979 , p. 211 .
[7] E. Cartan , Comptes Rendus , t. 174 , 1922 , p. 593 . JFM 48.0854.02 · JFM 48.0854.02
[8] B. Kostant , Lecture Notes Math. , t. 570 , 1975 , p. 177 . MR 580292 | Zbl 0358.53024 · Zbl 0358.53024
[9] M. Bachelor , Trans. Am. Math. Soc. , t. 253 , 1979 , p. 329 . MR 536951 | Zbl 0413.58002 · Zbl 0413.58002
[10] M. Bachelor , Trans. Am. Math. Soc. , t. 258 , 1980 , p. 257 . Zbl 0426.58003 · Zbl 0426.58003
[11] A. Pràstaro , Riv. Nuovo Cimento , t. 5 , n^\circ 4 , 1982 . MR 693882 | Zbl 0695.58028 · Zbl 0695.58028
[12] A. Pràstaro , Boll. Un. Mat. Ital. , t. 6 , 1 -B, 1982 , p. 1015 . MR 683489 | Zbl 0501.53023 · Zbl 0501.53023
[13] A. Pràstaro , Super-bundles of geometric objects, Yang-Mills gauge fields and SpinG- instantons (to appear).
[14] K. Gawedzki , Ann. Inst. Henri Poincaré , t. 27 , 1977 , p. 335 . Numdam | Zbl 0369.53061 · Zbl 0369.53061
[15] I. Vaisman , Cohomology and Differential Forms , N. Y ., 1973 . MR 341344 | Zbl 0267.58001 · Zbl 0267.58001
[16] P.J. Hilton and U. Stammbach , A Course in Homological Algebra , Springer-Verlag , Berlin , 1971 . MR 346025 | Zbl 0238.18006 · Zbl 0238.18006
[17] N. Bourbaki , Algèbre, I , Chapitres 1-3, Hermann , Paris 1970 . MR 274237 | Zbl 0211.02401 · Zbl 0211.02401
[18] H. Goldschmidt , J. Differential Geom. , t. 1 , 1967 , p. 269 . Zbl 0159.14101 · Zbl 0159.14101
[19] D.C. Spencer , Bull. Am. Math. Soc. , t. 75 , 1969 , p. 179 . MR 242200 | Zbl 0185.33801 · Zbl 0185.33801
[20] H. Lewy , Ann. Math. , t. 65 , n^\circ 1 , 1957 , p. 155 .
[21] W.J. Sweeney , Acta Math. , t. 120 , 1968 , p. 223 . MR 226662 | Zbl 0159.38402 · Zbl 0159.38402
[22] C. Ehresmann , Compt. Rendus Acad. Sc. , Paris , t. 240 , 1954 , p. 1762 ; t. 241 , 1955 , p. 397 and 1955 ; t. 246 , 1958 , p. 360 . MR 101284
[23] V. Guillemin , J. Differential Geom. , t. 1 , 1967 , p. 58 .
[24] A. Pràstaro , Boll. Un. Mat. Ital. , t. 5 , 17 -B, 1980 , p. 704 ; Boll. Un. Mat. Ital. , t. 5 , S.-FM, 1981 , p. 69 and 107 . MR 580551 | Zbl 0438.58004 · Zbl 0438.58004
[25] P.M. Quan , Introduction à la Géométrie des Variétés Différentielles , Dunod , Paris , 1969 . MR 242080
[26] R.G. Yates , Comm. Math. Phys. , t. 76 , 1980 , p. 255 . Article | MR 588049 | Zbl 0447.53027 · Zbl 0447.53027
[27] M.A. Awada , Comm. Math. Phys. , t. 91 , 1983 , p. 53 . Article | MR 719809 | Zbl 0529.53055 · Zbl 0529.53055
[28] R. Coquereaux , Phys. Lett. , t. 115 B, 1982 , p. 389 . MR 674730
[29] D’Auria , P. Fre’ and T. Regge , CERN Preprint TH.3563, 1983 .
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