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

1993/09/10 by Ali Mostafazadeh · 3 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #Quantum Mechanics and Non-Hermitian Physics #hep-th

paper · pdf · doi:10.1063/1.530630

published as J.Math.Phys. 35 (1994) 1095-1124 · 47 pages

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 Peierls bracket quantization scheme is applied to the supersymmetric system corresponding to the twisted spin index theorem. A detailed study of the quantum system is presented, and the Feynman propagator is exactly computed. The Green's function methods provide a direct derivation of the index formula. Note: This is essentially a new SUSY proof of the index theorem.

Citations

• On the heat equation and the index theorem
• Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr" odinger Equation

Cited by

• Supersymmetry and the Atiyah-Singer Index Theorem II: The Scalar Curvature Factor in the Schr" odinger Equation
• DIRAC OPERATOR ON COMPLEX MANIFOLDS AND SUPERSYMMETRIC QUANTUM MECHANICS
• On a -graded generalization of the Witten index