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Supersymmetric quantum theory and non-commutative geometry | | J. Froehlich
; O. Grandjean
; A. Recknagel
; | | Date: |
9 Jul 1998 | | Journal: | Commun.Math.Phys. 203 (1999) 119-184 | | Subject: | Mathematical Physics | math-ph hep-th math.MP | | Abstract: | Classical differential geometry can be encoded in spectral data, such as Connes’ spectral triples, involving supersymmetry algebras. In this paper, we formulate non-commutative geometry in terms of supersymmetric spectral data. This leads to generalizations of Connes’ non-commutative spin geometry encompassing non-commutative Riemannian, symplectic, complex-Hermitian and (Hyper-)Kaehler geometry. A general framework for non-commutative geometry is developed from the point of view of supersymmetry and illustrated in terms of examples. In particular, the non-commutative torus and the non-commutative 3-sphere are studied in some detail. | | Source: | arXiv, math-ph/9807006 | | Services: | Forum | Review | PDF | Favorites | |
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