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We elucidate the basic physical mechanisms responsible for the quantum-classical transition in one-dimensional, bounded chaotic systems subject to unconditioned environmental interactions. We show that such a transition occurs due to the…
Hamilton-Jacobi theory provides a natural starting point for a covariant description of the gravitational field. Using a spatial gradient expansion, one may solve for the phase of the wavefunction by using a line-integral in superspace.…
The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain…
In a quantum theory of cosmology spacetime behaves classically only in limited patches of the configuration space on which the wave function of the universe is defined. Quantum transitions can connect classical evolution in different…
Transition from quantum to semiclassical behaviour and loss of quantum coherence for inhomogeneous perturbations generated from a non-vacuum initial state in the early Universe is considered in the Heisenberg and the Schr\"odinger…
The formalism to treat quantization and evolution of cosmological perturbations of multiple fluids is described. We first construct the Lagrangian for both the gravitational and matter parts, providing the necessary relevant variables and…
We investigate the Wheeler-DeWitt equation for a flat, homogeneous, and isotropic Universe containing a canonical scalar field with a potential. We show that under the constraint $|\Psi|=1$, where the Wheeler-DeWitt equation exactly becomes…
Consistent dynamics which couples classical and quantum degrees of freedom exists, provided it is stochastic. This dynamics is linear in the hybrid state, completely positive and trace preserving. One application of this is to study the…
In this paper we present a new point of view on the mathematical foundations of statistical physics of infinite volume systems. This viewpoint is based on the newly introduced notions of transition energy function, transition energy field…
In many situations, one can approximate the behavior of a quantum system, i.e. a wave function subject to a partial differential equation, by effective classical equations which are ordinary differential equations. A general method and…
For zero energy, $E=0$, we derive exact, classical and quantum solutions for {\em all} power-law oscillators with potentials $V(r)=-\gamma/r^\nu$, $\gamma>0$ and $-\infty <\nu<\infty$. When the angular momentum is non-zero, these solutions…
Using Hamilton-Jacobi theory, we develop a formalism for solving semi-classical cosmological perturbations which does not require an explicit choice of time-hypersurface. The Hamilton-Jacobi equation for gravity interacting with matter…
Since there are quantization ambiguities in constructing the Hamiltonian constraint operator in isotropic loop quantum cosmology, it is crucial to check whether the key features of loop quantum cosmology, such as the quantum bounce and…
By employing special solutions of the Hamilton-Jacobi equation and tools from lattice theories, we suggest an approach to convert classical theories to quantum theories for mechanics and field theories. Some nontrivial results are obtained…
Positively-curved, oscillatory universes are studied within the context of Loop Quantum Cosmology subject to a consistent semi-classical treatment. The semi-classical effects are reformulated in terms of an effective phantom fluid with a…
We consider the Euclidean path integral approach to higher-derivative theories proposed by Hawking and Hertog (Phys. Rev. D65 (2002), 103515). The Pais-Uhlenbeck oscillator is studied in some detail. The operator algebra is reconstructed…
The author considers the planar rotational motion of the mathematical pendulum with its pivot oscillating both vertically and horizontally, so the trajectory of the pivot is an ellipse close to a circle. The analysis is based on the exact…
When the vacuum state of a scalar or electromagnetic field is modified by the presence of a reflecting boundary, an interacting test particle undergoes velocity fluctuations. Such effect is regarded as a sort of quantum analog of the…
The geometric framework for the Hamilton-Jacobi theory developed in previous works is extended for multisymplectic first-order classical field theories. The Hamilton-Jacobi problem is stated for the Lagrangian and the Hamiltonian formalisms…
Jordan-Brans-Dicke theories with a linearized potential for the scalar field are investigated in the framework of the stochastic approach. The fluctuations of this field are examined and their backreaction on the classical background is…