Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr{\" o}dinger Equation

Abstract

The quantization of the superclassical system used in the proof of the index theorem results in a factor of ${\hslash }^{2}R/8$ in the Hamiltonian. The path integral expression of the kernel is analyzed up to and including 2-loop order. The existence of the scalar curvature term is confirmed by comparing the linear term in the heat kernel expansion with the 2-loop order terms in the loop expansion.

19 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, part2

References in corpus (1)

• Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem

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