Related papers: Path integral and noncommutative poisson brackets
The existence of bi-Hamiltonian structures for the rational Harmonic Oscillator (non-central harmonic oscillator with rational ratio of frequencies) is analyzed by making use of the geometric theory of symmetries. We prove that these…
Reciprocal transformations of Hamiltonian operators of hydrodynamic type are investigated. The transformed operators are generally nonlocal, possessing a number of remarkable algebraic and differential-geometric properties. We apply our…
It is shown that the phase space path integral for a system with arbitrary second class constraints (primary, secondary ...) can be rewritten as a configuration space path integral of the exponent of the Lagrangian action with some local…
A path-integral approach to lattice polarons is developed. The method is based on exact analytical elimination of phonons and subsequent Monte Carlo simulation of self-interacting fermions. The analytical basis of the method is presented…
Gauge invariance of systems whose Hamilton-Jacobi equation is separable is improved by adding surface terms to the action fuctional. The general form of these terms is given for some complete solutions of the Hamilton-Jacobi equation. The…
In Hamiltonian time-dependent mechanics, the Poisson bracket does not define dynamic equations, that implies the corresponding peculiarities of describing time-dependent holonomic constraints. As in conservative mechanics, one can consider…
The eigenvalue problem of the spherically symmetric oscillator Hamiltonian is revisited in the context of canonical raising and lowering operators. The Hamiltonian is then factorized in terms of two not mutually adjoint factorizing…
Modified Hamiltonians are used in the field of geometric numerical integration to show that symplectic schemes for Hamiltonian systems are accurate over long times. For nonlinear systems the series defining the modified Hamiltonian usually…
The calculus of variation and the construction of path integrals is revisited within the framework of non-linear generalized functions. This allows us to make a rigorous analysis of the variation of an action that takes into account the…
A new method is proposed to generate nonlinear integrable systems by starting with existing Lax pair and a new form of Kr\"onecker product. It is observed that such equation can be generated with the help of a Hamiltonian structure.…
The non-holonomic deformations of non-local integrable systems belonging to the Nonlinear Schrodinger family are studied using the Bi-Hamiltonian formalism as well as the Lax pair method. The non-local equations are first obtained by…
A dynamical system framework is used to describe transport processes in plasmas embedded in a magnetic field. For periodic systems with one degree of freedom the Poincar\'e map provides a splitting of the phase space into regions where…
This contribution presents an integration method based on the Simpson quadrature. The integrator is designed for finite-dimensional nonlinear mechanical systems that derive from variational principles. The action is discretized using…
In this work we discuss the natural appearance of the Generalized Brackets in systems with non-involutive (equivalent to second class) constraints in the Hamilton-Jacobi formalism. We show how a consistent geometric interpretation of the…
In this paper we point out the existence of a remarkable nonlocal transformation between the damped harmonic oscillator and a modified Emden type nonlinear oscillator equation with linear forcing, $\ddot{x}+\alpha x\dot{x}+\beta x^3+\gamma…
Space-time non-commutative theories are non-local in time. We develop the Hamiltonian formalism for non-local field theories in d space-time dimensions by considering auxiliary d+1 dimensional field theories which are local with respect to…
Closed systems in Newtonian mechanics obey the principle of Galilean relativity. However, the usual Lagrangian for Newtonian mechanics, formed from the difference of kinetic and potential energies, is not invariant under the full group of…
The small oscillations of an arbitrary scleronomous system subject to time-independent non dissipative forces are discussed. The linearized equations of motion are solved by quadratures. As in the conservative case, the general integral is…
We discuss some special classes of canonical transformations of the extended phase space, which relate integrable systems with a common Lagrangian submanifold. Various parametric forms of trajectories are associated with different integrals…
A recent proposal to connect the loop quantization with the spin foam model for cosmology via the path integral is hereby adapted to the case of mechanical systems within the framework of the so called polymer quantum mechanics. The…