Related papers: The 'most classical' states of Euclidean invariant…
Gauge-invariant boundary conditions in Euclidean quantum gravity can be obtained by setting to zero at the boundary the spatial components of metric perturbations, and a suitable class of gauge-averaging functionals. This paper shows that,…
Familiar formulations of classical and quantum mechanics are shown to follow from a general theory of mechanics based on pure states with an intrinsic probability structure. This theory is developed to the stage where theorems from quantum…
By considering (non-relativistic) quantum mechanics as it is done in practice in particular in condensed-matter physics, it is argued that a deterministic, unitary time evolution within a chosen Hilbert space always has a limited scope,…
For the models of $N$-body identical harmonic oscillators interacting through potentials of homogeneous degree -2, the unitary operator that transforms a system of time-dependent parameters into that of unit spring constant and unit mass of…
Systems of classical continuous particles in the grand canonical ensemble interacting through purely attractive, yet stable, interactions are defined. By a lattice approximation, FKG ferromagnetic inequalities are shown to hold for such…
We investigate the uncertainty relation for estimating the position of one electron in a uniform magnetic field in the framework of the quantum estimation theory. Two kinds of momenta, canonical one and mechanical one, are used to generate…
Classical Koopman--von Neumann Hilbert spaces of states are constructed here by the action of classical random fields on a vacuum state in ways that support an action of the quantized electromagnetic field and of the $U(1)$--invariant…
The problem of how to obtain quasi-classical states for quantum groups is examined. A measure of quantum indeterminacy is proposed, which involves expectation values of some natural quantum group operators. It is shown that within any…
The geometric form of standard quantum mechanics is compatible with the two postulates: 1) The laws of physics are invariant under the choice of experimental setup and 2) Every quantum observation or event is intrinsically statistical.…
According to the Second Law of Thermodynamics, cycles applied to thermodynamic equilibrium states cannot perform work (passivity property of thermodyamic equilibrium states). In the presence of matter this can hold only in the rest frame of…
We investigate entanglement properties at quantum phase transitions of an integrable extended Hubbard model in the momentum space representation. Two elementary subsystems are recognized: the single mode of an electron, and the pair of…
It is believed that gravity will be explained in the framework of the existing quantum theory when one succeeds in eliminating divergencies at large momenta or small distances (although the phenomenon of gravity has been observed only at…
New status in quantum mechanics is connected with recent achievements in the inverse problem. With its help instead of about ten exactly solvable models which serve as a basis of the contemporary education there are infinite (!) number,…
Relativistic invariance in Euclidean formulations of quantum mechanics is discussed. Relativistic treatments of quantum theory are needed to study hadronic systems at sub-hadronic distance scales. Euclidean formulations of relativistic…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
In a previous paper, a project of constructing quantum models of classical properties has been started. The present paper concludes the project by turning to classical mechanics. The quantum states that maximize entropy for given averages…
Quantum operators of coordinates and momentum components of a particle in Minkowski space-time belong to a noncommutative algebra and give rise to a quantum phase space. Under some constraints, in particular, the Lorentz invariance…
We establish three impossibility results regarding our knowledge of the quantum state of the universe. Suppose the universal quantum state is a typical unit vector in a high-dimensional subspace $\mathscr{H}_0$ of Hilbert space…
A formal symmetry between generalized coordinates and momenta is postulated to formulate classical and quantum theories of a particle coupled to an Abelian gauge field. It is shown that the symmetry (a) requires the field to have dynamic…
To enhance the consistency between the quantum descriptions of waves and particles, we quantise mechanical point particles in this paper in the same physically-motivated way as we previously quantised light in quantum electrodynamics…