Integration on noncompact supermanifolds
HTML articles powered by AMS MathViewer
- by Mitchell J. Rothstein PDF
- Trans. Amer. Math. Soc. 299 (1987), 387-396 Request permission
Abstract:
We note that the Berezin integral, which is ill-defined for noncompact supermanifolds, is a distribution with support on the underlying manifold. This leads to the discovery of correction terms in the Berezinian transformation law and thereby eliminates the boundary ambiguities.References
- 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
- 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
- I. B. Penkov, ${\cal D}$-modules on supermanifolds, Invent. Math. 71 (1983), no. 3, 501–512. MR 695902, DOI 10.1007/BF02095989 J. M. Rabin, The Berezin integral as contour integral, Univ. of Chicago preprint, EF1 84/4.
- Alice Rogers, Consistent superspace integration, J. Math. Phys. 26 (1985), no. 3, 385–392. MR 786391, DOI 10.1063/1.526619
- Mitchell J. Rothstein, Deformations of complex supermanifolds, Proc. Amer. Math. Soc. 95 (1985), no. 2, 255–260. MR 801334, DOI 10.1090/S0002-9939-1985-0801334-0
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 299 (1987), 387-396
- MSC: Primary 58C50; Secondary 58A50
- DOI: https://doi.org/10.1090/S0002-9947-1987-0869418-5
- MathSciNet review: 869418