Classical and quantum gravity with fractional operators

Classical and Quantum Gravity

Integrable Classical and Quantum Gravity

In these lectures we report recent work on the exact quantization of dimensionally reduced gravity [1, 2, 3, 4]. Assuming the presence of commuting Killing symmetries which effectively eliminate the dependence on all but two space-time coordinates allows us to cast the models into the form of 2d non-linear (G/H)-coset space σ-models coupled to gravity and a dilaton. This construction includes a...

Classical Scale of Quantum Gravity

Characteristic length scale of the post-Newtonian corrections to the gravitational field of a body is given by its gravitational radius rg. The role of this scale in quantum domain is discussed in the context of the low-energy effective theory. The question of whether quantum gravity effects appear already at rg leads to the question of correspondence between classical and quantum theories, whi...

Classical Spacetime from Quantum Gravity

We show how classical spacetime emerges from quantum gravity through the study of a quantum FRW cosmological model coupled to a free massive scalar field using a new asymptotic expansion method of the Wheeler-DeWitt equation. It is shown that the coherent states of the nonadiabatic basis of a particular generalized invariant give rise to the quantum back reaction of matter field proportional to...

Quantum operators: A classical perspective

We review current research in the field of categorical quantum mechanics. We place the category of relations within the same categorical framework and point out the similarities with the category of Hilbert spaces. Subsequently, we provide a categorical model for investigating the spectral theorem (as provided in [22]), within the context of an internally diagonalisable element and apply these ...