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Zeitschriftenartikel

The graded product of real spectral triples

MPG-Autoren

Farnsworth,  Shane
AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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1605.07035.pdf
(Preprint), 569KB

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Zitation

Farnsworth, S. (2017). The graded product of real spectral triples. Journal of Mathematical Physics, 58: 023507. doi:10.1063/1.4975410.


Zitierlink: https://hdl.handle.net/11858/00-001M-0000-002D-238F-2
Zusammenfassung
Forming the product of two geometric spaces is one of the most basic operations in geometry, but in the spectral-triple formulation of non-commutative geometry, the standard prescription for taking the product of two real spectral triples is problematic: among other drawbacks, it is non-commutative, non-associative, does not transform properly under unitaries, and often fails to define a proper spectral triple. In this paper, we explain that these various problems result from using the ungraded tensor product; by switching to the graded tensor product, we obtain a new prescription where all of the earlier problems are neatly resolved: in particular, the new product is commutative, associative, transforms correctly under unitaries, and always forms a well defined spectral triple.