Related papers: A Quantum-Classical Brackets from p-Mechanics
The extraction of classical degrees of freedom in quantum mechanics is studied in the stochastic variational method. By using this classicalization, a hybrid model constructed from quantum and classical variables (quantum-classical hybrids)…
This paper presents the geometric setting of quantum variational principles and extends it to comprise the interaction between classical and quantum degrees of freedom. Euler-Poincar\'e reduction theory is applied to the Schr\"odinger,…
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…
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…
The mathematical possibility of coupling two quantum dynamic systems having two different Planck constants, respectively, is investigated. It turns out that such canonical dynamics are always irreversible. Semiclassical dynamics is obtained…
The Dirac method is used to analyze the classical and quantum dynamics of a particle constrained on a circle. The method of Lagrange multipliers is scrutinized, in particular in relation to the quantization procedure. Ordering problems are…
In the present paper fractional Hamilton-Jacobi equation has been derived for dynamical systems involving Caputo derivative. Fractional Poisson-bracket is introduced. Further Hamilton's canonical equations are formulated and quantum wave…
Representation of classical dynamics by unitary transformations has been used to develop unified description of hybrid classical-quantum systems with particular type of interaction, and to formulate abstract systems interpolating between…
It is shown that the vacuum state of weakly interacting quantum field theories can be described, in the Heisenberg picture, as a linear combination of randomly distributed incoherent paths that obey classical equations of motion with…
In this paper we present a survey of the use of differential geometric formalisms to describe Quantum Mechanics. We analyze Schroedinger and Heisenberg frameworks from this perspective and discuss how the momentum map associated to the…
We provide an overview of a canonical formalism that describes mixed quantum-classical systems in terms of statistical ensembles on configuration space, and discuss applications to measurement theory. It is shown that the formalism allows a…
The Heisenberg double of a Hopf algebra may be regarded as a quantum analogue of the cotangent bundle of a Lie group. Quantum duality principle describes relations between a Hopf algebra, its dual, and their Heisenberg double in a way which…
Nambu's construction of multi-linear brackets for super-integrable systems can be thought of as degenerate Poisson brackets with a maximal set of Casimirs in their kernel. By introducing privileged coordinates in phase space these…
We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson…
A version of quantum orbit method is presented for real forms of equal rank of quantum complex simple groups. A quantum moment map is constructed, based on the canonical isomorphism between a quantum Heisenberg algebra and an algebra of…
We show that the classical mechanics of an algebraic model are implied by its quantizations. An algebraic model is defined, and the corresponding classical and quantum realizations are given in terms of a spectrum generating algebra.…
In this paper, we further study the G-dynamics newly emerged in the covariant dynamics defined by the quantum covariant Poisson bracket (QCPB) theory. We propose three new operators based on the G-dynamics, we find that the non-Hermitian…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
In the context of our recently developed emergent quantum mechanics, and, in particular, based on an assumed sub-quantum thermodynamics, the necessity of energy quantization as originally postulated by Max Planck is explained by means of…
Quantum Field Theory (QFT) makes predictions by combining two sets of assumptions: (1) quantum dynamics, such as a Schrodinger or Liouville equation; (2) quantum measurement, such as stochastic collapse to an eigenfunction of a measurement…