Canonical transformation

About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.

New Canonical Variables for Orbital and Rotational Motions

Abstract: A new canonical transformation of freedom two was found. By using this, we derived three new sets of canonical variables for the orbital motion and two for the rotational motion. New canonical variables have clear physical meanings and remain well-defined in the case when the classical sets become ill-defined, for example, when the eccentricity and/or the inclination is small for the elliptic orbital motion.

On the canonical transformation in the theory of exciton–phonon interaction

Abstract: A canonical transformation which eliminates the trilinear exciton–phonon interaction and introduces new elementary excitations — “dressed” excitons — is proposed; it holds true both for the narrow and for broad exciton bands The energy spectrum of the dressed excitons is investigated in detail for a one-dimensional model of Frenkel excitons interacting with optical phonons Es wird eine kanonische Transformation vorgeschlagen, die die trilineare Exziton–Phonon-wechselwirkung eliminiert und neue Elementaranregungen, „bekleidete” Exzitonen, einfuhrt Dies gilt sowohl fur schmale als auch fur breite Exzitonenbanden Das Energiespektrum der bekleideten Exzitonen wird ausfuhrlich fur ein eindimensionales Modell von Frenkel-Exzitonen, die mit optischen Phononen wechselwirken, untersucht

Generalized Lagrangian of N=1 supergravity and its canonical constraints with the real Ashtekar variable

Abstract: We generalize the Lagrangian of $N=1$ supergravity (SUGRA) by using an arbitrary parameter $\ensuremath{\xi},$ which corresponds to the inverse of Barbero's parameter $\ensuremath{\beta}.$ This generalized Lagrangian involves the chiral one as a special case of the value $\ensuremath{\xi}=\ifmmode\pm\else\textpm\fi{}i.$ We show that the generalized Lagrangian gives the canonical formulation of $N=1$ SUGRA with the real Ashtekar variable after the $3+1$ decomposition of spacetime. This canonical formulation is also derived from those of the usual $N=1$ SUGRA by performing Barbero's type canonical transformation with an arbitrary parameter $\ensuremath{\beta}(={\ensuremath{\xi}}^{\ensuremath{-}1}).$ We give some comments on the canonical formulation of the theory.

An extended canonical perturbation method

Abstract: In this investigation, a procedure is described for extending the application of canonical perturbation theories, which have been applied previously to the study of conservative systems only, to the study of non-conservative dynamical systems. The extension is obtained by imbedding then-dimensional non-conservative motion in a 2n-dimensional space can always be specified in canonical form, and, consequently, the motion can be studied by direct application of any canonical perturbation method. The disadvantage of determining a solution to the 2n-dimensional problem instead of the originaln-dimensional problem is minimized if the canonical transformation theory is used to develop the perturbation solution. As examples to illustrate the application of the method, Duffing's equation, the equation for a linear oscillator with cubic damping and the van der Pol equation are solved using the Lie-Hori perturbation algorithm.