A Rogers 1992 J. Phys. A: Math. Gen. 25 6043 doi:10.1088/0305-4470/25/22/027
A Rogers
Show affiliationsFor pt.I see ibid., vol.25, p.447-68, (1992). 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.
02.40.Vh Global analysis and analysis on manifolds
02.40.Ky Riemannian geometries
05.30.Fk Fermion systems and electron gas
60H07 Stochastic calculus of variations and the Malliavin calculus
58A50 Supermanifolds and graded manifolds (See also 14A22, 32C11)
58B20 Riemannian, Finsler and other geometric structures (See also 53C20, 53C60)
81S25 Quantum stochastic calculus
58C50 Analysis on supermanifolds or graded manifolds
53C20 Global Riemannian geometry, including pinching (See also 31C12, 58B20)
Quantum gases, liquids and solids
Issue 22 (21 November 1992)
A Rogers 1992 J. Phys. A: Math. Gen. 25 6043
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