Related papers: Quantum geometry with intrinsic local causality
We propose a formulation of the holographic principle, suitable for a background independent quantum theory of cosmology. It is stated as a relationship between the flow of quantum information and the causal structure of a quantum…
General relativity is a background-independent theory of a dynamical classical spacetime geometry. Quantum theory is formulated in a classical spacetime, as an intrinsically probabilistic, contextual theory of non-classical, interfering…
Motivated by the expectation that relativistic symmetries might acquire quantum features in Quantum Gravity, we take the first steps towards a theory of ''Doubly'' Quantum Mechanics, a modification of Quantum Mechanics in which the…
Using tangent bundle geometry we construct an equivalent reformulation of classical field theory on flat spacetimes which simultaneously encodes the perspectives of multiple observers. Its generalization to curved spacetimes realizes a new…
We explain how quantum gravity can be defined by quantizing spacetime itself. A pinpoint is that the gravitational constant G = L_P^2 whose physical dimension is of (length)^2 in natural unit introduces a symplectic structure of spacetime…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Spin networks are at the core of quantum gravity. Our aim is to plug the mathematical community at large into the procedures turn to create a finite quantum theory of general relativity. For this, because of the different cultural…
Quantum gravity is studied nonperturbatively in the case in which space has a boundary with finite area. A natural set of boundary conditions is studied in the Euclidean signature theory, in which the pullback of the curvature to the…
We review quantum causal histories starting with their interpretations as a quantum field theory on a causal set and a quantum geometry. We discuss the difficulties that background independent theories based on quantum geometry encounter in…
A realistic measurement-free theory for the quantum physics of multiple qubits is proposed. This theory is based on a symbolic representation of a fractal state-space geometry which is invariant under the action of deterministic and locally…
Any canonical quantum theory can be understood to arise from the compatibility of the statistical geometry of distinguishable observations with the canonical Poisson structure of Hamiltonian dynamics. This geometric perspective offers a…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…
The usual quantization of a classical space-time field does not touch the non-geometrical character of quantum mechanics. We believe that the deep problems of unification of general relativity and quantum mechanics are rooted in this poor…
We describe the time evolution of quantum systems in a classical background space-time by means of a covariant derivative in an infinite dimensional vector bundle. The corresponding parallel transport operator along a timelike curve $\cC$…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
We analyze classical and quantum dynamics of a particle in 2d spacetimes with constant curvature which are locally isometric but globally different. We show that global symmetries of spacetime specify the symmetries of physical phase-space…
We propose uncertainty relations for the different coordinates of spacetime events, motivated by Heisenberg's principle and by Einstein's theory of classical gravity. A model of Quantum Spacetime is then discussed where the commutation…
Recent progress in quantum field theory and quantum gravity relies on mixed boundary conditions involving both normal and tangential derivatives of the quantized field. In particular, the occurrence of tangential derivatives in the boundary…
We discuss the meaning of background independence in quantum theories of gravity where geometry and gravity are emergent and illustrate the possibilities using the framework of quantum causal histories.
I argue that the conventional field theoretic notion of vacuum state is not valid in quantum gravity. The arguments use gravitational effective field theory, as well as results from string theory, particularly the AdS/CFT correspondence.…