Related papers: Observers seeing gravitational Hilbert spaces: abs…
The gravitational path integral on $S^2 \times S^2$ can be interpreted either as evaluating a contribution to the norm of the Hartle-Hawking wavefunction conditional on spatial $S^1 \times S^2$ topology, or the pair creation rate of black…
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not…
We introduce the notion of an orthocomplemented subspace of a Hilbert space H, that is, a pair of orthogonal closed subspaces of H, as a two-dimensional counterpart to the one-dimensional notion of a closed subspace of H. Orthocomplemented…
We discuss transformations generated by dynamical quantum systems which are bi-unitary, i.e. unitary with respect to a pair of Hermitian structures on an infinite-dimensional complex Hilbert space. We introduce the notion of Hermitian…
Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is…
We study a holographic theory of general spacetimes that does not rely on the existence of asymptotic regions. This theory is to be formulated in a holographic space. When a semiclassical description is applicable, the holographic space is…
The earlier approach is used for description of qubits and geometric phase parameters, the things critical in the area of topological quantum computing. The used tool, Geometric (Clifford) Algebra is the most convenient formalism for that…
We study two subspace systems in a separable infinite-dimensional Hilbert space up to (bounded) isomorphism. One of the main result of this paper is the following: Isomorphism classes of two subspace systems given by graphs of bounded…
It is proposed that the mathematical formalism that is most appropriate for the study of spatially non-integrable cosmological models is the transverse geometry of a one-dimensional foliation (congruence) defined by a physical observer. By…
The AdS/CFT correspondence states that certain conformal field theories are equivalent to string theories in a higher-dimensional anti-de Sitter space. One aspect of the correspondence is an equivalence of density matrices or, if one…
An abstract formulation of quantum dynamics in the presence of a general set of quantum constraints is developed. Our constructive procedure is such that the relevant projection operator onto the physical Hilbert space is obtained with a…
Whereas the nature of dark components in the Universe remains unknown, alternative models of gravity have been developed to offer a geometric explanation to the origin of such components. In this work we use the Minimal Geometric…
A discrete path integral formalism is used to obtain the transition amplitude between 'sources' (slits and detector) in the twin-slit experiment of quantum mechanics. This method explicates the normally tacit construct of dynamic entities…
Unlike flat space quantum field theories that focus on scattering amplitudes, the main observables in quantum cosmology are correlation functions. The systematic way of calculating correlators is called in-in formalism, which requires only…
It is congruous with the quantum nature of the world to view the space-time geometry as an emergent structure that shows classical features only at some observational level. One can thus conceive the space-time manifold as a purely…
The asymptotic structure of the gravitational field of isolated systems has been analyzed in great detail in the case when the cosmological constant $\Lambda$ is zero. The resulting framework lies at the foundation of research in diverse…
Complex states of quantum gravity in flat and AdS gravity can have features that are inaccessible to classical asymptotic observers. The missing information appears to such observers to be hidden behind a horizon or in a baby universe. Here…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
We give a review of recent work aimed at understanding the dynamics of gravitational collapse in quantum gravity. Its goal is to provide a non-perturbative computational framework for understanding the emergence of the semi-classical…
After a brief review of topological gravity, we present a superspace approach to this theory. This formulation allows us to recover in a natural manner various known results and to gain some insight into the precise relationship between…