Related papers: Quantum geometrodynamics with intrinsic time devel…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
We recently introduced a particular nonlinear generalization of quantum mechanics which has the property that it is exactly solvable in terms of the eigenvalues and eigenfunctions of the Hamiltonian of the usual linear quantum mechanics…
In the minisuperspace models of quantum cosmology, the absence of time in the Wheeler-DeWitt (constraint) equation, is the main point leading to the generally accepted conclusion that in the quantum cosmology there is no possibility to…
The classical theory of gravity predicts its own demise -- singularities. We therefore attempt to quantize gravitation, and present here a new approach to the quantization of gravity wherein the concept of time is derived by imposing the…
Following a bi-cylindrical model of geometrical dynamics, in the present study we show that Einstein gravitational equation leads to bi-geodesic description in an extended symmetrical time-space which fit Hubble expansion in a "microscopic"…
A set of diverse but mutually consistent results obtained in different settings has spawned a new view of loop quantum gravity and its physical implications, based on the interplay of operator calculations and effective theory: Quantum…
In order to resolve the measurement problem of Quantum Mechanics, non-unitary time evolution has been derived from the unitarity of standard quantum formalism. New wave functions of free and non-free quantum systems follow from Schroedinger…
We propose a mathematical structure, based on a noncommutative geometry, which combines essential aspects of general relativity and quantum mechanics, and leads to correct "limiting cases" of both these theories. We quantize a groupoid…
Standard general coordinate invariance for the volume element is extended to general coordinate transformations that have a negative jacobian. This is possible by introducing a non Riemannian Measure of integration, which transforms…
Non-Hermiticity in quantum Hamiltonians leads to nonunitary time evolution and possibly complex energy eigenvalues, which can lead to a rich phenomenology with no Hermitian counterpart. In this work, we study the dynamics of an exactly…
The geometrical formulation of the quantum Hamilton-Jacobi theory shows that the quantum potential is never trivial, so that it plays the r\^ole of intrinsic energy. Such a key property selects the Wheeler-DeWitt (WDW) quantum potential…
The Hamiltonian formulation of general relativity (GR) is considered in finite space-time and a specific frame of reference given by the diffeo-invariant components of the Fock simplex in terms of the Dirac -- ADM variables. The evolution…
Observed physical phenomena can be described well by quantum mechanics or general relativity. People may try to find an unified fundamental theory which mainly aims to merge gravity with quantum theory. However, difficulty in merging those…
In previous work we discussed the quantization of paths in spacetime. Building on these ideas we have developed a mathematically coherent theory addressing a number of open questions concerning Loop Quantum Gravity. Our approach develops a…
The possibility has been recently demonstrated to manufacture (nonrelativistic, Hamiltonian) many-body problems which feature an isochronous time evolution with an arbitrarily assigned period $T$ yet mimic with good approximation, or even…
The requirement of general covariance of quantum field theory (QFT) naturally leads to quantization based on the manifestly covariant De Donder-Weyl formalism. To recover the standard noncovariant formalism without violating covariance,…
`How do our ideas about quantum mechanics affect our understanding of spacetime?' This familiar question leads to quantum gravity. The complementary question is also important: `How do our ideas about spacetime affect our understanding of…
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
(Abridged Abstract) This paper deals with a number of technical achievements that are instrumental for a dis-solution of the so-called {\it Hole Argument} in general relativity. The work is carried through in metric gravity for the class of…
The accepted idea that the expansion of the universe is accelerating needs, for compatibility to general relativity, the introduction of some unusual forms of matter. However, several authors have proposed that instead of making weird…