Exploring the Causal Structures of Almost Commutative Geometries

Abstract

We investigate the causal relations in the space of states of almost commutative Lorentzian geometries. We fully describe the causal structure of a simple model based on the algebra $\mathcal{S}({\mathbb{R}}^{1,1})\otimes M_2(\mathbb{C})$, which has a non-trivial space of internal degrees of freedom. It turns out that the causality condition imposes restrictions on the motion in the internal space. Moreover, we show that the requirement of causality favours a unitary evolution in the internal space.

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Cited by in corpus (14)

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• Causality for nonlocal phenomena
• Wick Rotation and Fermion Doubling in Noncommutative Geometry
• Spectral action with zeta function regularization
• Causality in noncommutative two-sheeted space-times
• The noncommutative geometry of Zitterbewegung
• Metrics and causality on Moyal planes
• Noncommutative geometry, Lorentzian structures and causality
• The disappearance of causality at small scale in almost-commutative manifolds
• Lorentzian Connes Distance, Spectral Graph Distance and Loop Gravity
• Families of spectral triples and foliations of space(time)
• Space and time dimensions of algebras with applications to Lorentzian noncommutative geometry and quantum electrodynamics
• Quantum causality constraints on kappa-Minkowski space-time
• Quantum causality in $\kappa$-Minkowski and related constraints