Spectral dimension with deformed spacetime signature

Understand

Studies of the effective regime of loop quantum gravity (LQG) revealed that, in the limit of Planckian curvature scales, spacetime may undergo a transition from the Lorentzian to Euclidean signature.

• This effect is a consequence of quantum modifications of the hypersurface deformation algebra, which in the linearized case is equivalent to a deformed version of the Poincar\'e algebra.
• In this paper the latter relation is applied to the LQG-inspired hypersurface deformation algebra that is characterized by the above mentioned signature change.
• While the exact form of the deformed Poincar\'e algebra is not uniquely determined, the algebra under consideration is representative enough to capture a number of qualitative features.