Related papers: Canonical transformations and minimal length
We prove that small deformations of canonical singularities are canonical.
Poisson bracket relations for generators of canonical transformations are derived directly from the Galilei and Poincar\'e groups of changes of space-time coordinates. The method is simple but rigorous. The meaning of each step is clear…
Canonical commutation relations for the Bateman-Hillion type nondispersive wave packets are constructed
Three elementary canonical transformations are shown both to have quantum implementations as finite transformations and to generate, classically and infinitesimally, the full canonical algebra. A general canonical transformation can, in…
The covariant canonical formalism is a covariant extension of the traditional canonical formalism of fields. In contrast to the traditional canonical theory, it has a remarkable feature that canonical equations of gauge theories or gravity…
In this paper, we present Poisson brackets of certain classes of mappings obtained as general periodic reductions of integrable lattice equations. The Poisson brackets are derived using the so called Ostrogradsky transformation.
Canonical transformation in a three-dimensional phase space endowed with Nambu bracket is discussed in a general framework. Definition of the canonical transformations is constructed as based on canonoid transformations. It is shown that…
In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…
We find that in presence of noncommutative poisson brackets the relation between Lagrangian and Hamiltonian is modified. We discuss this property by using the path integral formalism for non-relativistic systems. We apply this procedure to…
We analyze the canonical treatment of classical constrained mechanical systems formulated with a discrete time. We prove that under very general conditions, it is possible to introduce nonsingular canonical transformations that preserve the…
We argue that reducing nonlinear programming problems to a simple canonical form is an effective way to analyze them, specially when the problem is degenerate and the usual linear independence hypothesis does not hold. To illustrate this…
In this paper, we propose a new deformed Poisson brackets which leads to the Fock coordinate transformation by using an analogous procedure as in Deformed Special Relativity. We therefore derive the corresponding momentum transformation…
We point out that a certain finite size effect in heavy ion physics, the canonical enhancement, is based on the difference of conservation constrained pair statistics for Poisson and Gauss distributions, respectively. Consequently it should…
Realizations of algebras in terms of canonical or bosonic variables can often be used to simplify calculations and to exhibit underlying properties. There is a long history of using such methods in order to study symmetry groups related to…
We construct Poisson brackets at boundaries of open strings and membranes with constant background fields which are compatible with their boundary conditions. The boundary conditions are treated as primary constraints which give infinitely…
Quantum canonical transformations are defined in analogy to classical canonical transformations as changes of the phase space variables which preserve the Dirac bracket structure. In themselves, they are neither unitary nor non-unitary. A…
In this paper we study the problem of Hamiltonization of nonholonomic systems from a geometric point of view. We use gauge transformations by 2-forms (in the sense of Severa and Weinstein [29]) to construct different almost Poisson…
We discuss trivial deformations of the canonical Poisson brackets associated with the Toda lattices, relativistic Toda lattices, Henon-Heiles, rational Calogero-Moser and Ruijsenaars-Schneider systems and apply one of these deformations to…
Easy steps through essential Hamiltonian dynamics are outlined, from necessary definitions of Poisson brackets and canonical transformations, to a quick proof that Hamiltonian evolution is made by canonical transformations, the quickest…
In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations…