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Finite-dimensional Quantum Mechanics can be geometrically formulated as a proper classical-like Hamiltonian theory in a projective Hilbert space. The description of composite quantum systems within the geometric Hamiltonian framework is…
Vacuum spherically symmetric Einstein gravity in $N\ge 4$ dimensions can be cast in a two-dimensional conformal nonlinear sigma model form by first integrating on the $(N-2)$-dimensional (hyper)sphere and then performing a canonical…
Currently, dynamics of a massive macroparticle is given by classical analytical mechanics (CM), while that of a massive micro one is given by quantum mechanics (QM). We propose a mechanics effective for both: We transform, under coordinate…
Last years a certain attention was attracted to the statement that Hamiltonian formulations of General Relativity, in which different parametrizations of gravitational variables were used, may not be related by a canonical transformation.…
Constructing a classical mechanical system associated with a given quantum mechanical one, entails construction of a classical phase space and a corresponding Hamiltonian function from the available quantum structures and a notion of…
It is argued that the world is a dissipative dynamic system, a phase flow of which is formed by conformally-symplectic mapping. The key assumption is that the concept of energy in microcosm makes sense only for the steady motions…
We study a class of Hamiltonian deformations of the massless Einstein-Klein-Gordon system in spherical symmetry for which the Dirac constraint algebra closes. The system may be regarded as providing effective equations for quantum…
We derive formulas for variations of mass, angular momentum and canonical energy in Einstein (n-2)-gauge form field theory by means of the ADM formalism. Considering the initial data for the manifold with an interior boundary which has the…
We consider a non-minimally coupled Einstein-Maxwell gravity with no $U(1)$ symmetry property to study stability of an electrostatic star via canonical quantization approach and obtain that the stability is free of gauge field effects. By…
In this first of a series of four articles, it is shown how a hamiltonian quantum dynamics can be formulated based on a generalization of classical probability theory using the notion of quasi-invariant measures on the classical phase space…
We construct a U(1) gerbe with a connection over a finite-dimensional, classical phase space P. The connection is given by a triple of forms A,B,H: a potential 1-form A, a Neveu-Schwarz potential 2-form B, and a field-strength 3-form H=dB.…
The requirements are formulated which lead to the existence of the class of globally regular solutions to the minimally coupled GR equations which are asymptotically de Sitter at the center. The brief review of the resulting geometry is…
We treat space and time as bona fide quantum degrees of freedom on an equal footing in Hilbert space. Motivated by considerations in quantum gravity, we focus on a paradigm dealing with linear, first-order Hamiltonian and momentum…
Recently, we have suggested some semi-quantitative Hamiltonian for an electron in a hydrogen atom in a weak gravitational field, which takes into account quantum effects of electron motion in the atom. We have shown that this Hamiltonian…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are reviewed using pure gravity in three dimensions as a toy model. The classical part focusses on the role of observers in general…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
Cosmological solutions for covariant canonical gauge theories of gravity are presented. The underlying covariant canonical transformation framework invokes a dynamical space-time Hamiltonian consisting of the Einstein-Hilbert term plus a…
We re-investigate how generic off-diagonal cosmological solutions depending, in general, on all spacetime coordinates can be constructed in massive and f-modified gravity using the anholonomic frame deformation method. There are constructed…
A general formalism for understanding the thermodynamics of horizons in spherically symmetric spacetimes is developed. The formalism reproduces known results in the case of black hole spacetimes. But its power lies in being able to handle…