Related papers: Generalized Schroedinger equation in Euclidean fie…
A model of genome evolution is proposed. Based on three assumptions the evolutionary theory of a genome is formulated. The general law on the direction of genome evolution is given. Both the deterministic classical equation and the…
In this paper is considered a generalized quantization principle for the gravitational field in canonical quantum gravity, especially with respect to quantum geometrodynamics. This assumption can be interpreted as a transfer from the…
We study solutions to the Cauchy problem for the linear and nonlinear Schroedinger equation with a quadratic Hamiltonian depending on time. For the linear case the evolution operator can be expressed as an integral operator with the…
Usually quantum theory is formulated in terms of the evolution of states through spacelike surfaces. However, a generalization of this formulation is needed for field theory in spacetimes not foliable by spacelike surfaces, or in quantum…
Quantum mechanics with a generalized uncertainty principle arises through a representation of the commutator $[\hat{x}, \hat{p}] = i f(\hat{p})$. We apply this deformed quantization to free scalar field theory for $f_\pm =1\pm \beta p^2$.…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is of continuing interest. Practically it is of importance for the interpretation of multi-particle coincidence measurements performed at macroscopic…
The wave-function in quantum gravity is supposed to obey the Wheeler-DeWitt (WDW) equation, however there is neither a satisfactory probability interpretation nor a successful solution to the problem of time in the WDW framework. To gain…
The evolution equation is used as the fundamental equation of field theory, which is described entirely by the geometry of the four-dimensional space. The evolution kernel determines the covariant action of physical fields by the proper…
We investigate quantum effects in the evolution of general systems. For studying such temporal quantum phenomena, it is paramount to have a rigorous concept and profound understanding of the classical dynamics in such a system in the first…
We investigate the inverse problem concerning the evolution of a qubit system, specifically we consider how one can establish the Hamiltonians that account for the evolution of a qubit along a prescribed path in the projected Hilbert space.…
We study formulation and probabilistic interpretation of a simple general-relativistic hamiltonian quantum system. The system has no unitary evolution in background time. The quantum theory yields transition probabilities between measurable…
For linear scalar field theories, I characterize those classical Hamiltonian vector fields which have self-adjoint operators as their quantum counterparts. As an application, it is shown that for a scalar field in curved space-time (in a…
The Lagrangians and Hamiltonians of classical field theory require to comprise gauge fields in order to be form-invariant under local gauge transformations. These gauge fields have turned out to correctly describe pertaining elementary…
This is the first paper in a series aimed to implement boundary conditions consistent with the constraints' propagation in 3D numerical relativity. Here we consider spherically symmetric black hole spacetimes in vacuum or with a minimally…
The space of density matrices is embedded in a Euclidean space to deduce the dynamical equation satisfied by the state of an open quantum system. The Euclidean norm is used to obtain an explicit expression for the speed of the evolution of…
Time evolution is formulated and discussed in the framework of Schroeder's functional equation. The proposed method yields smooth, continuous dynamics without the prior need for local propagation equations.
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
In this treatise I introduce the time dependent Generalized Born's Rule for the probabilities of quantum events, including conditional and consecutive probabilities, as the unique fundamental time evolution equation of quantum theory. Then…
We first recall that the system of fluid mechanics equations (Euler and continuity) that describes a fluid in irrotational motion subjected to a generalized quantum potential (in which the constant is no longer reduced to the standard…
We analyze some consequences of two possible interpretations of the action of the ladder operators emerging from generalized Heisenberg algebras in the framework of the second quantized formalism. Within the first interpretation we…