Canonical transformation

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

Improved linear representation of surface waves. Part 2. Slowly varying bottoms and currents

Abstract: We extend the results of a previous paper to fluids of finite depth. We consider the Hamiltonian theory of waves on the free surface of an incompressible fluid, and derive the canonical transformation that eliminates the leading order of nonlinearity for finite depth. As in the previous paper we propose using the Lie transformation method since it seems to include a nearly correct implementation of short waves interacting with long waves. We show how to use the Eikonal method for slowly varying currents and/or depths in combination with the nonlinear transformation. We note that nonlinear effects are more important in water of finite depth. We note that a nonlinear action conservation law can be derived. 10 refs.

Canonical transformations for constrained systems

Abstract: A standard procedure for transition from Lagrangian to Hamiltonian description of constrained dynamics was proposed by the author in [1]. This work shows that the procedure allows one to clarify the canonical transformation sense in phase space for these systems and, in particular, to describe the Lagrangian class which gives the same dynamics.

Matrix models for D-particle dynamics and the string/black hole transition

Abstract: For a generic two-dimensional OA string background, we map the Dirac-Bom-Infeld action to a matrix model. This is achieved using a canonical transformation. The action describes D0-branes in this background, while the matrix model has a potential which encodes all the information of the background geometry. We apply this formalism to specific backgrounds: for Rindler space, we obtain a matrix model with an upside-down quadratic potential, while for AdS 2 space, the potential is linear. Furthermore we analyse the black hole geometry with RR flux. In particular, we show that at the Hagedorn temperature, the resulting matrix model coincides with the one for the linear dilaton background. We interpret this result as a realization of the string/black hole transition.

Gluon condensates from the Hamiltonian formalism

Abstract: We derive recently obtained relations connecting the logarithmic gauge coupling derivative of the hadron mass and the cosmological constant to the matter and vacuum gluon condensates, within a Hamiltonian framework. The key idea is a canonical transformation which brings the relevant part of the Hamiltonian into a suitable form. We have checked that the transformation is free from rescaling anomalies. The Hamiltonian framework allows one to extend these connections to the case of direct product gauge groups relevant to the Standard Model for example. Furthermore, we illustrate the relations within the Schwinger model and super Yang–Mills theory (Seiberg–Witten theory).

A structure-preserving algorithm for the minimum H ∞ norm computation of finite-time state feedback control problem

Abstract: The algorithm being developed here is based on the generating function approach for finite-time H ∞ control and application of canonical transformation of linear Hamiltonian system. First, an equivalent finite-time H ∞ control law in terms of the third-type generating function is derived. Then, by using symplectic structure of the Hamiltonian system's state transition matrix, a group of matrix recursive formulae are deduced for the evaluation of the finite-time H ∞ control law. Combining with a matrix singularity testing procedure, this recursive algorithm verifies the existence condition of sub-optimal H ∞ controllers and gives the minimum H ∞ norm of finite-time control systems. Inherited from the canonical transformation, the matrix recursive formulae have a standard symplectic form; this structure-preserving property helps facilitate reliable and effective computation. Numerical results show the effectiveness of the proposed algorithm.