STOCHASTIC CALCULUS IN SUPERSPACE .2. DIFFERENTIAL FORMS, SUPERMANIFOLDS AND THE ATIYAH-SINGER INDEX THEOREM

被引：18
作者：
ROGERS, A
机构：
[1] Dept. of Math., King's Coll., London
来源：
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 1992年 / 25卷 / 22期
关键词：
D O I：
10.1088/0305-4470/25/22/027
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Starting with vector bundles over manifolds, supermanifolds are constructed whose function algebras correspond to twisted differential forms. Stochastic calculus for bosonic and fermionic Brownian paths is used to provide a geometric construction of Brownian paths on these supermanifolds. A Feynman-Kac formula for the heat kernel of the Laplace-Beltrami operator is then derived. This is used to provide a simple, rigorous version of the supersymmetric proofs of the Atiyah-Singer index theorem.
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页码：6043 / 6062
页数：20
相关论文
共 26 条
[1]   SUPERSYMMETRY AND THE ATIYAH-SINGER INDEX THEOREM [J].
ALVAREZGAUME, L .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 90 (02) :161-173
[2]  
[Anonymous], 1987, SCHRODINGER OPERATOR
[3]  
Bartocci C., 1991, KLUWER ACADMIC PUBLI, V71, DOI DOI 10.1007/978-94-011-3504-7
[4]  
BATCHELOR M, 1983, MATH ASPECTS SUPERSP
[5]  
BEREZIN FA, 1966, METHOD 2ND QUANTIZAT
[6]  
Berline N., 2003, HEAT KERNELS DIRAC O
[7]   THE ATIYAH-SINGER THEOREMS - A PROBABILISTIC APPROACH .1. THE INDEX THEOREM [J].
BISMUT, JM .
JOURNAL OF FUNCTIONAL ANALYSIS, 1984, 57 (01) :56-99
[8]  
ELWORTHY KD, 1988, LECTURE NOTES MATH, V1362
[9]   PSEUDODIFFERENTIAL-OPERATORS ON SUPERMANIFOLDS AND THE ATIYAH-SINGER INDEX THEOREM [J].
GETZLER, E .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 92 (02) :163-178
[10]   A SHORT PROOF OF THE LOCAL ATIYAH-SINGER INDEX THEOREM [J].
GETZLER, E .
TOPOLOGY, 1986, 25 (01) :111-117
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