相关论文: Factorizations of one dimensional classical system…
A generalization of classical mechanics is obtained from a complex parametrization of the phase space. The formalism supports complex Hamiltonian functions describing non-conservative classical mechanical systems. A quantization scheme that…
One classical theory, as determined by an equation of motion or set of classical trajectories, can correspond to many unitarily {\em in}equivalent quantum theories upon canonical quantization. This arises from a remarkable ambiguity, not…
In this paper we consider a generalized classical mechanics with fractional derivatives. The generalization is based on the time-clock randomization of momenta and coordinates taken from the conventional phase space. The fractional…
The formulation of classical mechanics applicable to fermionic degrees of freedom is presented in mathematically rigorous terms, including a description of how the mathematical structure relates to the quantization of the theory. Canonical…
In recent years, many natural Hamiltonian systems, classical and quantum, with constants of motion of high degree, or symmetry operators of high order, have been found and studied. Most of these Hamiltonians, in the classical case, can be…
Recently, there has been an increasing interest in modelling and computation of physical systems with neural networks. Hamiltonian systems are an elegant and compact formalism in classical mechanics, where the dynamics is fully determined…
We construct integrals of motion for multidimensional classical systems from ladder operators of one-dimensional systems. This method can be used to obtain new systems with higher order integrals. We show how these integrals generate a…
In this work, we investigate generic classical two-dimensional (2D) superintegrable Hamiltonian systems H, characterized by the existence of three functionally independent integrals of motion (I_0=H,I_1,I_2). Our main result, formulated and…
The integrals of motion of the classical two dimensional superintegrable systems with quadratic integrals of motion close in a restrained quadratic Poisson algebra, whose the general form is investigated. Each classical superintegrable…
The factorization technique for superintegrable Hamiltonian systems is revisited and applied in order to obtain additional (higher-order) constants of the motion. In particular, the factorization approach to the classical anisotropic…
We discuss the classical and quantum mechanical evolution of systems described by a Hamiltonian that is a function of a solvable one, both classically and quantum mechanically. The case in which the solvable Hamiltonian corresponds to the…
In this work simple and effective quantization procedure of classical dynamical systems is proposed and illustrated by a number of examples. The procedure is based entirely on differential equations which describe time evolution of systems.
The purpose of this work is to present a method based on the factorizations used in one dimensional quantum mechanics in order to find the symmetries of quantum and classical superintegrable systems in higher dimensions. We apply this…
We develop new constructions of 2D classical and quantum superintegrable Hamiltonians allowing separation of variables in Cartesian coordinates. In classical mechanics we start from two functions on a one-dimensional phase space, a natural…
We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum…
The Jacobi theta-functions admit a definition through the autonomous differential equations (dynamical system); not only through the famous Fourier theta-series. We study this system in the framework of Hamiltonian dynamics and find…
The classical Hamilton equations of motion yield a structure sufficiently general to handle an almost arbitrary set of ordinary differential equations. Employing elementary algebraic methods, it is possible within the Hamiltonian structure…
We study a certain class of bulk-boundary systems in the Batalin-Vilkovisky (BV) formalism. We construct factorization algebras of observables for such bulk-boundary systems, and show that these factorization algebras have a natural Poisson…
We study classical Hamiltonian systems in which the intrinsic proper time evolution parameter is related through a probability distribution to the physical time, which is assumed to be discrete. - This is motivated by the ``timeless''…
The quantization method based on the quantum Hamiltonian Jacobi equation, is extended to two-dimensional non-separable but integrable Hamiltonians. It is shown that each wave function for those systems corresponds to a well-defined family…