Related papers: Lagrangian formalism and classical statistical ens…
A reductive structure is associated here with Lagrangian canonically defined conserved quantities on gauge-natural bundles. Parametrized transformations defined by the gauge-natural lift of infinitesimal principal automorphisms induce a…
We show that, in spite of a rather common opinion, quantum mechanics can be represented as an approximation of classical statistical mechanics. The approximation under consideration is based on the ordinary Taylor expansion of physical…
We develop a functional-analytical machinery for studying the quadratic regulator problem arising from spectra perturbations of infinite-dimensional dynamical systems. In particular, we are interested in applications to inertial manifolds…
We discuss the condition for the validity of equilibrium quantum statistical mechanics in the light of recent developments in the understanding of classical and quantum chaotic motion. In particular, the ergodicity parameter is shown to…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
In this note we present invariant formulation of the d'Alambert principle and classical time-dependent Lagrangian mechanics with holonomic constraints from the perspective of moving frames.
We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical…
A strong analog classical simulation of general quantum evolution is proposed, which serves as a novel scheme in quantum computation and simulation. The scheme employs the approach of geometric quantum mechanics and quantum informational…
This paper develops numerical methods for optimal control of mechanical systems in the Lagrangian setting. It extends the theory of discrete mechanics to enable the solutions of optimal control problems through the discretization of…
The main goal of these lectures is to introduce and review the Hamiltonian formalism for classical constrained systems and in particular gauge theories. Emphasis is put on the relation between local symmetries and constraints and on the…
Connecting ideas of geometric formulation of quantum mechanics with new results in symplectic geometry a new approach to geometrical quantization procedure is proposed. As a first result we verify that the correspondence between "classical"…
We extend some aspects of the Hamilton-Jacobi theory to the category of stochastic Hamiltonian dynamical systems. More specifically, we show that the stochastic action satisfies the Hamilton-Jacobi equation when, as in the classical…
Quantum mechanics is essentially a statistical theory. Classical mechanics, however, is usually not viewed as being inherently statistical. Nevertheless, the latter can also be formulated statistically. Furthermore, a statistical…
We construct a lagrangian geometric formulation for first-order field theories using the canonical structures of first-order jet bundles, which are taken as the phase spaces of the systems in consideration. First of all, we construct all…
We present an alternative formalism of quantum mechanics tailored to statistical ensemble in phase space. The purpose of our work is to show that it is possible to establish an alternative autonomous formalism of quantum mechanics in phase…
By generalizing the cosymplectic setting for time-dependent Lagrangian mechanics, we propose a geometric framework for the Lagrangian formulation of classical field theories with a Lagrangian depending on the independent variables. For that…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
A path-integral quantization method is proposed for dynamical systems whose classical equations of motion do \textit{not} necessarily follow from the action principle. The key new notion behind this quantization scheme is the Lagrange…
We investigate the possibility that the semiclassical limit of quantum mechanics might be correctly described by a classical dynamical theory, other than standard classical mechanics. Using a set of classicality criteria proposed in a…
Starting from the 4-dimensional gluodynamics, we discuss the statistical ensemble of torons ( the toron is a self-dual solution with fractional topological number; it can be understood as a point defect) which interact strongly. It is shown…