Product of real spectral triples

Details Product of real spectral triples Product of real spectral triples

2010-11-19

arxiv.org/abs/1011.4456v1

Int. J. Geom. Methods Mod. Phys. - Vol. 8, No. 8 (2011) 1833-1848

Physics

Mathematical Physics

18 pages; based on the talk given at the conference "Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Se

Scientific paper

10.1142/S021988781100597X

We construct the product of real spectral triples of arbitrary finite dimension (and arbitrary parity) taking into account the fact that in the even case there are two possible real structures, in the odd case there are two inequivalent representations of the gamma matrices (Clifford algebra), and in the even-even case there are two natural candidates for the Dirac operator of the product triple.

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