Related papers: Canonical transformations and squeezing formalism …
The representation of a Schrodinger equations as a classic Hamiltonian system allows to construct a unified perturbation theory both in classic, and in a quantum mechanics grounded on the theory of canonical transformations, and also to…
A general classical theorem is presented according to which all invariant relations among the space time metric scalars, when turned into functions on the Phase Space of full Pure Gravity (using the Canonical Equations of motion), become…
We perform a canonical analysis of the system of 2d vacuum dilatonic black holes. Our basic variables are closely tied to the spacetime geometry and we do not make the field redefinitions which have been made by other authors. We present a…
Quantum canonical transformations are defined algebraically outside of a Hilbert space context. This generalizes the quantum canonical transformations of Weyl and Dirac to include non-unitary transformations. The importance of non-unitary…
Dynamics of ideal fluid with free surface can be effectively solved by perturbing the Hamiltonian in weak nonlinearity limit. However it is shown that perturbation theory, which includes third and fourth order terms in the Hamiltonian,…
Recently a Hamiltonian formulation for the evolution of the universe dominated by multiple oscillatory scalar fields was developed by the present author and was applied to the investigation of the evolution of cosmological perturbations on…
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. In this way, a physical clock with discrete…
We develop a complete Hamiltonian approach to the theory of perturbations around any spatially homogeneous spacetime. We employ the Dirac method for constrained systems which is well-suited to cosmological perturbations. We refine the…
We study the non-canonical symplectic structure, or K-symplectic structure inherited by the charged particle dynamics. Based on the splitting technique, we construct non-canonical symplectic methods which is explicit and stable for the…
We address an apparent conflict between the traditional canonical quantization framework of quantum theory and the spatially restricted quantum dynamics, when the translation invariance of the otherwise free quantum system is broken by…
We perform the canonical analysis of the Holst action for general relativity with a cosmological constant without introducing second-class constraints. Our approach consists in identifying the dynamical and nondynamical parts of the…
This article is concerned with analytic Hamiltonian dynamical systems in infinite dimension in a neighborhood of an elliptic fixed point. Given a quadratic Hamiltonian, we consider the set of its analytic higher order perturbations. We…
I study the canonical formulation and quantization of some simple parametrized systems, including the non-relativistic parametrized particle and the relativistic parametrized particle. Using Dirac's formalism I construct for each case the…
Canonical variables for the Poisson algebra of quantum moments are introduced here, expressing semiclassical quantum mechanics as a canonical dynamical system that extends the classical phase space. New realizations for up to fourth order…
Canonical vacuum gravity is expressed in generally-covariant form in order that spacetime diffeomorphisms be represented within its equal-time phase space. In accordance with the principle of general covariance, the time mapping ${\T}:…
We consider classical and quantum mechanics for an extended Heisenberg algebra with additional canonical commutation relations for position and momentum coordinates. In our approach this additional noncommutativity is removed from the…
In the paper is presented an invariant quantization procedure of classical mechanics on the phase space over flat configuration space. Then, the passage to an operator representation of quantum mechanics in a Hilbert space over…
For the Toda lattice and the Holt system we consider properties of canonical transformations of the extended phase space, which preserve integrability. The separated variables are invariant under change of the time. On the other hand,…
We analyse the canonical quantum dynamics of the isotropic universe, as emerging from the Hamiltonian formulation of a metric f(R) gravity, viewed in the Jordan frame. The canonical method of quantization is performed by solving the…
This work propose an alternative and systematic way to obtain a canonical Lagrangian formulation for rotational systems. This will be done in the symplectic framework and with the introduction of extra variables which enlarge the phase…