Grading of Spinor Bundles and Gravitating Matter in Non-Commutative Geometry

Details Grading of Spinor Bundles and Gravitating Matter in Non-Commutative Geometry Grading of Spinor Bundles and Gravitating Matter in Non-Commutative Geometry

1993-04-30

arxiv.org/abs/hep-th/9304157v1

Lett. Math. Phys. 30 (1994) 259-266

Physics

High Energy Physics

High Energy Physics - Theory

9 pages, LaTeX, PRA-HEP-93/6

Scientific paper

10.1007/BF00751062

The gravitating matter is studied within the framework of the non-commutative geometry. The non-commutative Einstein-Hilbert action on the product of a four dimensional manifold with a discrete space gives the models of matter fields coupled to the standard Einstein gravity.The matter multiplet is encoded in the Dirac operator which yields the representation of the algebra of the universal forms. The general form of the Dirac operator depends on a choice of the grading of the corresponding spinor bundle. A choice is given, which leads to the nonlinear vector sigma-model coupled to the Einstein gravity.

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