Abstract:
We reconsider differential geometry from the point of view of the quantum theory of non-relativistic spinning particles, which provides examples of supersymmetric quantum mechanics. This enables us to encode geometrical structure in algebraic data consisting of an algebra of functions on a manifold and a family of supersymmetry generators represented on a Hilbert space. We show that known types of differential geometry can be classified in terms of the supersymmetries they exhibit. Our formulation is tailor-made for a generalization to non-commutative geometry, which will be presented in a separate paper.
Similar content being viewed by others
Author information
Authors and Affiliations
Additional information
Received: 1 April 1997 / Accepted: 13 September 1997
Rights and permissions
About this article
Cite this article
Fröhlich, J., Grandjean, O. & Recknagel, A. Supersymmetric Quantum Theory and Differential Geometry . Comm Math Phys 193, 527–594 (1998). https://doi.org/10.1007/s002200050339
Issue Date:
DOI: https://doi.org/10.1007/s002200050339