Supersymmetry and Morse theory

1982/01/01 by Edward Witten · 26 citations
Mathematics · Physics and Astronomy · #Computer science #Mathematical economics #Mathematical physics #Mathematics #Morse code #Morse theory #Noncommutative and Quantum Gravity Theories #Physics #Pure mathematics #Quantum Mechanics and Non-Hermitian Physics #Quantum chaos and dynamical systems #Supersymmetry #Theoretical physics

paper · pdf · doi:10.4310/jdg/1214437492

crossref issued 1982/01/01 · crossref published 1982/01/01 · crossref published-print 1982/01/01 · openalex publication_date 1982/01/01 · crossref created 2017/03/16 · crossref deposited 2021/05/09 · openalex created_date 2025/10/10 · crossref indexed 2026/07/31 · openalex updated_date 2026/08/05

Abstract

It is shown that the Morse inequalities can be obtained by consideration of a certain supersymmetric quantum mechanics Hamiltonian.Some of the implications of modern ideas in mathematics for supersymmetric theories are discussed.

Citations

• The Index of Elliptic Operators: III
• A Lefschetz Fixed Point Formula for Elliptic Complexes: I
• Search for a realistic Kaluza-Klein theory
• A Lefschetz Fixed Point Formula for Elliptic Complexes: II. Applications
• The Index of Elliptic Operators: I
• The Index of Elliptic Operators: II

Cited by

• Loop Hori Formulae for T-duality and Twisted Bismut-Chern Character
• Transformation de Fourier, constantes d'équations fonctionnelles et conjecture de Weil
• The fluid manifesto: emergent symmetries, hydrodynamics, and black holes
• Kinematic dynamo, supersymmetry breaking, and chaos
• Introduction to Supersymmetric Theory of Stochastics
• Perspectives on geometric analysis
• The Atiyah—Singer theorems: A probabilistic approach. I. The index theorem
• Pseudodifferential operators on supermanifolds and the Atiyah-Singer index theorem
• Fluctuation relations in simple examples of non-equilibrium steady states
• Morse theory indomitable
• Topological quantum field theory
• Topological quantum field theory
• Supersymmetry and Representation Theory in Low Dimensions
• Towards Noncommutative Topological Quantum Field Theory:Tangential Hodge-Witten cohomology
• Geometric phase in supersymmetric quantum mechanics
• More (thoughts on) Gribov copies
• An instanton-invariant for 3-manifolds
• Witten's complex and infinite-dimensional Morse theory
• Morse theory for Lagrangian intersections
• Symplectic fixed points and holomorphic spheres
• Floer theory and low dimensional topology
• Atiyah–Singer index theorem [wikipedia]
• Morse theory [wikipedia]
• Perverse sheaf [wikipedia]
• Topological quantum field theory [wikipedia]
• Weil conjectures [wikipedia]