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

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

1993-09-10

arxiv.org/abs/hep-th/9309061v1

J.Math.Phys. 35 (1994) 1125-1138

Physics

High Energy Physics

High Energy Physics - Theory

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

Scientific paper

10.1063/1.530631

The quantization of the superclassical system used in the proof of the index theorem results in a factor of $\hbar^{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.

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