Book Review
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Marjorie Batchelor, Two approaches to supermanifolds, Trans. Amer. Math. Soc. 258 (1980), no. 1, 257–270. MR 554332, DOI 10.1090/S0002-9947-1980-0554332-9
F. A. Berezin, The method of second quantization, Pure and Applied Physics, Vol. 24, Academic Press, New York-London, 1966. Translated from the Russian by Nobumichi Mugibayashi and Alan Jeffrey. MR 0208930
[3] -, Introduction to superanalysis, Reidel, Dordrecht, 1987.
F. A. Berezin and G. I. Kac, Lie groups with commuting and anticommuting parameters, Mat. Sb. (N.S.) 82 (124) (1970), 343–359 (Russian). MR 0265520
[5] F. A. Berezin and D. A. Leites, Supermanifolds, Soviet Math. Dokl. 6 (1976), 1218-1222.
S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. B 62 (1976), no. 3, 335–337. MR 411531, DOI 10.1016/0370-2693(76)90089-7
Bryce DeWitt, Supermanifolds, Cambridge Monographs on Mathematical Physics, Cambridge University Press, Cambridge, 1984. MR 778559
Daniel Z. Freedman, P. van Nieuwenhuizen, and S. Ferrara, Progress toward a theory of supergravity, Phys. Rev. D (3) 13 (1976), no. 12, 3214–3218. MR 462449, DOI 10.1103/PhysRevD.13.3214
Atsushi Inoue and Yoshiaki Maeda, Foundations of calculus on super Euclidean space $\textbf {R}^{m|n}$ based on a Fréchet-Grassmann algebra, Kodai Math. J. 14 (1991), no. 1, 72–112. MR 1099318, DOI 10.2996/kmj/1138039340
Bertram Kostant, Graded manifolds, graded Lie theory, and prequantization, Differential geometrical methods in mathematical physics (Proc. Sympos., Univ. Bonn, Bonn, 1975) Lecture Notes in Math., Vol. 570, Springer, Berlin, 1977, pp. 177–306. MR 0580292
D. A. Leĭtes, Introduction to the theory of supermanifolds, Uspekhi Mat. Nauk 35 (1980), no. 1(211), 3–57, 255 (Russian). MR 565567
J. L. Martin, The Feynman principle for a Fermi system, Proc. Roy. Soc. London Ser. A 251 (1959), 543–549. MR 109640, DOI 10.1098/rspa.1959.0127
Alice Rogers, A global theory of supermanifolds, J. Math. Phys. 21 (1980), no. 6, 1352–1365. MR 574696, DOI 10.1063/1.524585
Alice Rogers, Super Lie groups: global topology and local structure, J. Math. Phys. 22 (1981), no. 5, 939–945. MR 622840, DOI 10.1063/1.525001
Mitchell J. Rothstein, The axioms of supermanifolds and a new structure arising from them, Trans. Amer. Math. Soc. 297 (1986), no. 1, 159–180. MR 849473, DOI 10.1090/S0002-9947-1986-0849473-8
Abdus Salam and J. Strathdee, Super-gauge transformations, Nuclear Phys. B76 (1974), 477–482. MR 0356737, DOI 10.1016/0550-3213(74)90537-9
[17] D. V. Volkov and V. P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett B 46 (1973), 109-110.
J. Wess and B. Zumino, Supergauge transformations in four dimensions, Nuclear Phys. B70 (1974), 39–50. MR 0356830, DOI 10.1016/0550-3213(74)90355-1
Peter West, Introduction to supersymmetry and supergravity, 2nd ed., World Scientific Publishing Co., Inc., Teaneck, NJ, 1990. MR 1112396, DOI 10.1142/1002
- [1]
- M. Batchelor, Two approaches to supermanifolds, Trans. Amer. Math. Soc. 258 (1980), 257-270. MR 554332 (81f:58001)
- [2]
- F. A. Berezin, The method of second quantization, Academic Press, New York, 1966. MR 0208930 (34:8738)
- [3]
- -, Introduction to superanalysis, Reidel, Dordrecht, 1987.
- [4]
- F. A. Berezin and G. I. Kac, Lie groups with commuting and anticommuting parameters, Math. USSR Sb. 11 (1970), 311. MR 0265520 (42:429)
- [5]
- F. A. Berezin and D. A. Leites, Supermanifolds, Soviet Math. Dokl. 6 (1976), 1218-1222.
- [6]
- S. Deser and B. Zumino, Consistent supergravity, Phys. Lett. B 62 (1976), 335. MR 0411531 (53:15264)
- [7]
- B. S. DeWitt, Supermanifolds, Cambridge Univ. Press, London and New York, 1984. MR 778559 (87b:58007)
- [8]
- S. Ferrera, D. Freedman, and P. van Nieuwenhuizen, Progress towards a theory of supergravity, Phys. Rev. D (3) 13 (1976), 3214. MR 0462449 (57:2422)
- [9]
- A. Inoue and Y. Maeda, Foundations of calculus on super euclidean space
based on a Fréchet-Grassmann algebra, Kodai Math. J. 14 (1991), 72-112. MR 1099318 (93c:58034)
- [10]
- B. Kostant, Graded manifolds, graded Lie theory and prequantization, Differential Geometric Methods in Mathematical Physics, Lecture Notes in Math., vol. 570, Springer-Verlag, New York, 1977. MR 0580292 (58:28326)
- [11]
- D. A. Leites, Introduction to the theory of supermanifolds, Russian Math. Surv. 35 (1980), 1-64. MR 565567 (81j:58003)
- [12]
- J. Martin, The feynman principle for a fermi system, Proc. Roy. Soc. London Ser. A, 251 (1959), 543-549. MR 0109640 (22:526)
- [13]
- A. Rogers, A global theory of supermanifolds, J. Math. Phys. 21 (1980), 1352-1365. MR 574696 (82d:58001)
- [14]
- -, Super Lie groups: global topology and local structure, J. Math. Phys. 22 (1981), 939-945. MR 622840 (83a:22021)
- [15]
- M. Rothstein, The axioms of supermanifolds and a new structure arising from them, Trans. Amer. Math. Soc. 297 (1986), 159-180. MR 849473 (87m:58015)
- [16]
- Abdus Salam and J. Strathdee, Supergauge transformations, Nuclear Phys. B Proc. Suppl. (1974). MR 0356737 (50:9206)
- [17]
- D. V. Volkov and V. P. Akulov, Is the neutrino a Goldstone particle?, Phys. Lett B 46 (1973), 109-110.
- [18]
- J. Wess and B. Zumino, Supergauge transformations in four dimensions, Nuclear Phys. B 70 (1974), 39. MR 0356830 (50:9299)
- [19]
- Peter West, Introduction to supersymmetry and supergravity, World Scientific, Singapore, 1990. MR 1112396 (92f:81004)
Review Information:
Reviewer:
Alice Rogers
Journal:
Bull. Amer. Math. Soc.
28 (1993), 184-189
DOI:
https://doi.org/10.1090/S0273-0979-1993-00352-5
