1212.5171 (Nicolas Franco)

Causality for Spectral Triple on Minkowski spacetime    [PDF]

Nicolas Franco

We propose the construction of a specific cone of Hermitian elements within a Lorentzian spectral triple which should be sufficient to define a notion of causality in noncommutative geometry. Such cone is based on an algebraic condition given by the Dirac operator and a fundamental symmetry. We prove that, for a Lorentian spectral triple constructed from the Minkowski spacetime, the usual notion of causality can be recovered. Then we extend the result to the Moyal-Minkowski spacetime and discuss some properties of causality for noncommutative spacetimes.

View original: http://arxiv.org/abs/1212.5171