Related papers: Dynamical Systems induced by Canonical Divergence …
This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…
Two different Hamiltonian formulations of the metric gravity are discussed and applied to describe a free gravitational field in the $d$ dimensional Riemann space-time. Theory of canonical transformations, which relate equivalent…
The claim that there is an inconsistency of quantum-classical dynamics [1] is investigated. We point out that a consistent formulation of quantum and classical dynamics which can be used to describe quantum measurement processes is already…
It is shown how a integrable mechanical system provides all the localized static solutions of a deformation of the linear O(N)-sigma model in two space-time dimensions. The proof is based on the Hamilton-Jacobi separability of the…
We show the equivalence of inverse problems for different dynamical systems and corresponding canonical systems. For canonical system with general Hamiltonian we outline the strategy of studying the dynamic inverse problem and procedure of…
The aim of this work is to show that particle mechanics, both classical and quantum, Hamiltonian and Lagrangian, can be derived from few simple physical assumptions. Assuming deterministic and reversible time evolution will give us a…
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…
Quantization of energy balance equations, which describe a separatrix -- like motion is presented. The method is based on an exact canonical transformation of the energy--time pair to the action-angle canonical pair, $ (E,t)\to (I,\theta)…
Gyroscopic systems in classical and quantum field theory are characterized by the presence of at least two scalar degrees of freedom and by terms that mix fields and their time derivatives in the quadratic Lagrangian. In Minkowski…
A new geometric approach to systems with boundary energy flow is developed using infinite-dimensional Dirac structures within the Lagrangian formalism. This framework satisfies a list of consistency criteria with the geometric setting of…
A simple mathematical procedure is introduced which allows redefining in an exact way divergent integrals and limits that appear in the basic equations of classical electrodynamics with point charges. In this way all divergences are at once…
In their seminal paper (Phys. Rev.121, 920 (1961)) Sudarshan, Mathews and Rau investigated properties of the dynamical $A$ and $B$ maps acting on $n$ dimensional quantum systems. Nature of the dynamical maps in open quantum system…
Canonical transformations are ubiquitous in Hamiltonian mechanics, since they not only describe the fundamental invariance of the theory under phase-space reparameterisations, but also generate the dynamics of the system. In the first part…
The covariant canonical transformation theory applied to the relativistic Hamiltonian theory of classical matter fields in dynamical space-time yields a novel (first order) gauge field theory of gravitation. The emerging field equations…
We observe that a wide class of higher-derivative systems admits a bounded integral of motion that ensures the classical stability of dynamics, while the canonical energy is unbounded. We use the concept of a Lagrange anchor to demonstrate…
We present several recent results concerning the transition between quantum and classical mechanics, in the situation where the underlying dynamical system has an hyperbolic behaviour. The special role of invariant manifolds will be…
We derive the dynamics of several rigid bodies of arbitrary shape in a 2-dimensional inviscid and incompressible fluid, whose vorticity field is given by point vortices. We adopt the idea of Vankerschaver et al. (2009) to derive the…
Stochastic kinematic description of a complex dynamics is shown to dictate an energetic and thermodynamic structure. An energy function $\varphi(x)$ emerges as the limit of the generalized, nonequilibrium free energy of a Markovian dynamics…
Information geometrical structure $(g^{(D_\alpha)}, \nabla^{(D_\alpha)},\nabla^{(D_\alpha)*})$ induced from the sandwiched R\'enyi $\alpha$-divergence $D_\alpha(\rho\|\sigma):=\frac{1}{\alpha (\alpha-1)}\log\,{\rm Tr}…
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.…