Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr" odinger Equation

1993/09/10 by Ali Mostafazadeh · 2 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #hep-th

paper · pdf · doi:10.1063/1.530631

published as J.Math.Phys. 35 (1994) 1125-1138 · 19 pages, Dep. of Physics, Uni. of Texas at Austin, Austin, Texas 78712, part2

arxiv created 1993/09/10 · openalex publication_date 1994/03/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The quantization of the superclassical system used in the proof of the index theorem results in a factor of ℏ²R/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.

Citations

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

Cited by

• Supersymmetry and the Atiyah-Singer Index Theorem I: Peierls Brackets, Green's Functions, and a Supersymmetric Proof of the Index Theorem
• DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS