Related papers: Constrained projective quantum states for the dege…
Gleason-type theorems for quantum theory allow one to recover the quantum state space by assuming that (i) states consistently assign probabilities to measurement outcomes and that (ii) there is a unique state for every such assignment. We…
Instead of formulating the state space of a quantum field theory over one big Hilbert space, it has been proposed by Kijowski [Kijowski 1977] to represent quantum states as projective families of density matrices over a collection of…
Recently, uniqueness theorems were constructed for the representation used in Loop Quantum Gravity. We explore the existence of alternate representations by weakening the assumptions of the so called LOST uniqueness theorem. The weakened…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
We apply a recent proposal for defining states and observables in quantum gravity to simple models. First, we consider a Klein-Gordon particle in an ex- ternal potential in Minkowski space and compare our proposal to the theory ob- tained…
A quantum system whose internal Hamiltonian is not strongly regular or/and control Hamiltonians are not full connected, are thought to be in the degenerate cases. In this paper, convergence problems of the multi-control Hamiltonians closed…
After a long technical and consequently philosophical disgression about the necessity of the construction presented in this book, a logically consistent and precise theory of quantum gravity is presented. The construction of this theory…
Relative entropy serves as a fundamental measure of state distinguishability in both quantum information theory and relativistic quantum field theory. Despite its conceptual importance, however, explicit computations of relative entropy…
Quantum gravity is an important and to great extent unsolved problem. There are many different approaches to the quantization of the metric field, both perturbative and non-perturbative. The current situation in the perturbative quantum…
We show that the set of states of the Ashtekar-Isham-Lewandowski holonomy algebra defined by elements of the Ashtekar-Lewandowski Hilbert space is dense in the space of all states. We consider weak convergence properties of a modified…
It is seen that issues of unitarity raised by the evolution of the wave function in curved spacetime can be resolved by describing the evolution of quantum states in Minkowski tangent space. The treatment adheres closely to the orthodox…
The state function of a quantum object is undetermined with respect to its phase. This indeterminacy does not matter if it is global, but what if the components of the state have unknown relative phases? Can useful computations be performed…
State-dependent gauge principle invoked to realize the relativity to a measuring device, has been proposed. Self-consistent global (cosmic) potential forms the state space of the fundamental field and its connection, agreed with…
The apparent impossibility of extending non-relativistic quantum mechanics to a relativistic quantum theory is shown to be due to the insufficient structural richness of the field of complex numbers over which quantum mechanics is built. A…
In this paper we introduce a projective invarinat measure on the special unitary group. It is directly related to transition probabilities. It has some interesting connection with convex geometry. Applications to approximation of quantum…
Despite the fact that quantum gravity is non-renormalisable, a consistent and mathematically rigorous construction of a perturbation series is possible. This is based on the use of the Batalin-Vilkovisky-Becchi-Rouet-Stora-Tyutin formalism…
Quantum states in the Earth's gravitational field were observed, when ultra-cold neutrons fall under gravity. The experimental results can be described by the quantum mechanical scattering model as it is presented here. We also discuss…
Quantum theory does not only predict probabilities, but also relative phases for any experiment, that involves measurements of an ensemble of systems at different moments of time. We argue, that any operational formulation of quantum theory…
This article reviews the present status of the spin foam approach to the quantization of gravity. Special attention is payed to the pedagogical presentation of the recently introduced new models for four dimensional quantum gravity. The…
Different constructions for Hilbert state space for constrained systems are investigated. Properties of Gaussian states analogous to quantum mechanical Gaussian wave functions are studied. Their evolution for quadratic Hamiltonian case are…