Related papers: Quantization, Holography and the Universal Coeffic…
Holographic duality describes gravitational theories in terms of quantum many-body systems. In holography, quantum information theory provides a crucial tool that directly connects microscopic structures of these systems to the geometries…
The quantum analogue of general relativistic geometry should be implementable on smooth manifolds without an a priori metric structure, the kinematical covariance group acting by diffeomorphisms. Here I approach quantum gravity (QG) in the…
We define a new construct in quantum field theory - the causal density matrix - obtained from the singularity structure of correlators of local operators. This object provides a necessary and sufficient condition for a quantum field theory…
We carry out a generalization of quantum group co-representations in order to encode in this structure those cases where non-commutativity between endomorphism matrix entries and quantum space coordinates happens.
One of the hallmarks of quantum theory is the realization that distinct measurements cannot in general be performed simultaneously, in stark contrast to classical physics. In this context the notions of coexistence and joint measurability…
As quantum technologies advance, the ability to generate increasingly large quantum states has experienced rapid development. In this context, the verification and estimation of large entangled systems represents one of the main challenges…
Quantum correlations in a composite system can be measured by resorting to a geometric approach, according to which the distance from the state of the system to a suitable set of classically correlated states is considered. Here we show…
This dissertation reviews several recent advances at the intersection of quantum information and holography. In holography, properties of quantum systems admit a gravitational interpretation via the AdS/CFT correspondence. For holographic…
A model of 3-dimensional topological quantum field theory is rigorously constructed. The results are applied to an explicit formula for deformation quantization of any finite-dimensional Lie bialgebra over the field of complex numbers. This…
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…
The Weyl-Wigner-Groenewold-Moyal formalism of deformation quantization is applied to the closed Friedmann-Lema\^itre-Robertson-Walker (FLRW) cosmological model. We show that the phase space average for the surface of the apparent horizon is…
We describe a refined version of a previous proposal for the exploration of quantum gravity phenomenology. Unlike the original scheme, the one presented here is free from sign ambiguities while it shares with the previous one the essential…
Quantum cosmology is the quantum theory of the entire universe. Although strange at first sight, it is appropriate because (1) our world appears to be fundamentally quantum, (2) the classical description of gravity breaks down at…
Finding the eigenstates of the total Hamiltonian H or its diagonalization is the important problem of quantum physics. However, in relativistic quantum field theory (RQFT) its complete and exact solution is possible for a few simple models…
The existing relation between the tomographic description of quantum states and the convolution algebra of certain discrete groupoids represented on Hilbert spaces will be discussed. The realizations of groupoid algebras based on qudit,…
The fact that quantum theory is non-differentiable, while general relativity is built on the assumption of differentiability sources an incompatibility between quantum theory and gravity. Higher order geometry addresses this issue directly…
A new approach is demonstrated that QFTs can be UV finite if they are viewed as the low energy effective theories of a fundamental underlying theory (that is complete and well-defined in all respects) according to the nowaday's standard…
Invited contribution to the Encyclopedia of Mathematical Physics (2nd edition), providing an overview over some main ideas and results in quantum cosmology. Key points: Canonical quantisation of homogeneous, isotropic cosmology; discussion…
A non-perturbative quantum field theory of General Relativity is presented which leads to a new realization of the theory of Covariant Quantum-Gravity (CQG-theory). The treatment is founded on the recently-identified Hamiltonian structure…
The problems encountered in trying to quantize the various cosmological models, are brought forward by means of a concrete example. The Automorphism groups are revealed as the key element through which G.C.T.'s can be used for a general…