Product of real spectral triples

Abstract

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.

18 pages; based on the talk given at the conference "Noncommutative Geometry and Quantum Physics, Vietri sul Mare, Aug 31 - Sept 5, 2009"

References in corpus (5)

• Why the Standard Model
• Ab Initio Study of 40Ca with an Importance Truncated No-Core Shell Model
• A superfluid helium converter for accumulation and extraction of ultracold neutrons
• Quantum Gravity Boundary Terms from Spectral Action of Noncommutative Space
• Dynamic critical behavior of the worm algorithm for the Ising model

Cited by in corpus (12)

• On Pythagoras' theorem for products of spectral triples
• The graded product of real spectral triples
• Spectral Noncommutative Geometry, Standard Model and all that
• Real structures on almost-commutative spectral triples
• Dirac operator on noncommutative principal circle bundles
• Lifting spectral triples to noncommutative principal bundles
• On twisted reality conditions
• Dirac operators for matrix algebras converging to coadjoint orbits
• Twisted reality and the second-order condition
• Real dimensional spaces in noncommutative geometry
• Real Spectral Triples on Crossed Products
• Lifting Bratteli Diagrams between Krajewski Diagrams: Spectral Triples, Spectral Actions, and $AF$ algebras