Related papers: Canonical description of quantum dynamics
The act of describing how a physical process changes a system is the basis for understanding observed phenomena. For quantum-mechanical processes in particular, the affect of processes on quantum states profoundly advances our knowledge of…
In a previous preprint (quant-ph/0012122) we introduced a ``contextual objectivity" formulation of quantum mechanics (QM). A central feature of this approach is to define the quantum state in physical rather than in mathematical terms, in…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
A geometric framework for describing quantum particles on a possibly curved background is proposed. Natural constructions on certain distributional bundles (`quantum bundles') over the spacetime manifold yield a quantum ``formalism'' along…
It is shown that quantum mechanics on noncommutative spaces (NQM) can be obtained by the canonical quantization of some underlying second class constrained system formulated in extended configuration space. It leads, in particular, to an…
In statistical mechanics, it is well known that finite-state classical lattice models can be recast as quantum models, with distinct classical configurations identified with orthogonal basis states. This mapping makes classical statistical…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
Recent developments in quantum computing suggest that it could be possible to make conditional changes to the state of a quantum mechanical system without resorting to classical observation. It is accomplished through collective response of…
An analysis of classical mechanics in a complex extension of phase space shows that a particle in such a space can behave in a way redolant of quantum mechanics; additional degrees of freedom permit 'tunnelling' without recourse to…
We present a reformulation of quantum mechanics in terms of probability measures and functions on a general classical sample space and in particular in terms of probability densities and functions on phase space. The basis of our proceeding…
We first recall a fact which is well-known among mathematical physicists although lesser-known among theoretical physicists that the standard quantum mechanics over a complex Hilbert space, is a Hamiltonian mechanics, regarding the Hilbert…
It is shown that quantum mechanics on noncommutative (NC) spaces can be obtained by canonical quantization of some underlying constrained systems. Noncommutative geometry arises after taking into account the second class constraints…
We generalize classical statistical mechanics to describe the kinematics and the dynamics of systems whose variables are constrained by a single quantum postulate (discreteness of the spectrum of values of at least one variable of the…
A novel theory of hybrid quantum-classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum-classical phase space. Both, the quantum and the classical descriptions of the respective…
A new realist interpretation of quantum mechanics is introduced. Quantum systems are shown to have two kinds of properties: the usual ones described by values of quantum observables, which are called extrinsic, and those that can be…
The phase space of quantum mechanics can be viewed as the complex projective space endowed with a Kaehlerian structure given by the Fubini-Study metric and an associated symplectic form. We can then interpret the Schrodinger equation as…
The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…
In order to study quantum dynamics of the FRW-universe of closed type, definitions of velocity, Hubble function and duration of the evolved universe are introduced into cosmology. The proposed definitions are characterized by high stability…
Quantum particles and classical particles are described in a common setting of classical statistical physics. The property of a particle being "classical" or "quantum" ceases to be a basic conceptual difference. The dynamics differs,…
Several years ago the so-called quantum geometrodynamics in extended phase space was proposed. The main role in this version of quantum geometrodynamics is given to a wave function that carries information about geometry of the Universe as…