Quantum causality in $\kappa$-Minkowski and related constraints

Abstract

We study quantum causal structures in $1+1$ $\kappa$-Minkowski space-time described by a Lorentzian Spectral Triple whose Dirac operator is built from a natural set of twisted derivations of the $\kappa$-Poincaré algebra. We show that the Lorentzian Spectral Triple must be twisted to accommodate the twisted nature of the derivations. We exhibit various interesting classes of causal functions, including an analog of the light-cone coordinates. We show in particular that the existence of a causal propagation between two pure states, the quantum analogs of points, can exist provided quantum constraints, linking the momentum and the space coordinate, are satisfied. One of these constraints is a quantum analog of the speed of light limit.

25 pages. Misprints corrected. An enlarged physical discussion has been included. Final version to be published

References in corpus (7)

• Type III and spectral triples
• Gauge theories on quantum spaces
• Causality in noncommutative two-sheeted space-times
• The noncommutative geometry of Zitterbewegung
• Noncommutative geometry, Lorentzian structures and causality
• Past and future blurring at fundamental length scale
• Twisted Spectral Triples without the First-Order Condition

Cited by in corpus (1)

• Noncommutative Lightcones from Quantum SO(2,1) Conformal Groups