Canonical transformation

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

A nine-fold canonical decomposition for linear systems

Abstract: The zero structure for non-minimal proper systems in state-space form is investigated. The approach is ‘ geometric ’, and a complete characterization in geometric terms is given of the invariant, decoupling, system and transmission zeros, as defined by Rosenbrock. The first main result is a formula for the transmission zeros. Second, a ‘ canonical ’ lattice diagram is presented of a decomposition of the state space which can be viewed as the ‘ product ’ of the Kalman canonical decomposition and the Morse canonical decomposition. This decomposition gives a straightforward characterization of all zeros just mentioned in terms of spectral properties of subspaces under a certain class of feedback and injection mappings. Via this diagram a number of equivalent formulae for the transmission zeros are derived. The freedom in pole assignment leads to new characterizations for the invariant and system zeros in terms of greatest common divisors of characteristic polynomials. Finally, the relation is demonstrated be...

Nonrelativistic Green's Function for Systems with Position-Dependent Mass

Abstract: Given a spatially dependent mass, we obtain the 2-point Green's function for exactly solvable nonrelativistic problems. This is accomplished by mapping the wave equation for these systems into well-known exactly solvable Schrodinger equations with constant mass using point canonical transformation. The one-dimensional oscillator class is considered and examples are given for several mass distributions.

Structure of the MHV-rules lagrangian

Abstract: Recently, a canonical change of field variables was proposed that converts the Yang-Mills Lagrangian into an MHV-rules Lagrangian, i.e. one whose tree level Feynman diagram expansion generates CSW rules. We solve the relations defining the canonical transformation, to all orders of expansion in the new fields, yielding simple explicit holomorphic expressions for the expansion coefficients. We use these to confirm explicitly that the three, four and five point vertices are proportional to MHV amplitudes with the correct coefficient, as expected. We point out several consequences of this framework, and initiate a study of its implications for MHV rules at the quantum level. In particular, we investigate the wavefunction matching factors implied by the Equivalence Theorem at one loop, and show that they may be taken to vanish in dimensional regularisation.

Construction of mappings for Hamiltonian systems and their applications

Abstract: Basics of Hamiltonian Mechanics- Perturbation Theory for Nearly Integrable Systems- Mappings for Perturbed Systems- Method of Canonical Transformation for Constructing Mappings- Mappings Near Separatrix Theory- Mappings Near Separatrix Examples- The KAM Theory Chaos Nontwist and Nonsmooth Maps- Rescaling Invariance of Hamiltonian Systems Near Saddle Points- Chaotic Transport in Stochastic Layers- Magnetic Field Lines in Fusion Plasmas- Mapping of Field Lines in Ergodic Divertor Tokamaks- Mappings of Magnetic Field Lines in Poloidal Divertor Tokamaks- Miscellaneous

Motion of a particle in a ring-shaped potential: an approach via a nonbijective canonical transformation

Abstract: The problem of a particle in the three-dimensional ring-shaped potential ησ2(2a0/r − ηa/r2 sin2 θ)e0 introduced by Hartmann is transformed into the problem of a coupled pair two-dimensional harmonic oscillators with inverse quadratic potentials by using a nonbijective canonical transformation, viz., the Kustaanheimo–Stiefel transformation. The energy E of the levels for the ring-shaped potential is obtained in a straightforward way from the one for the two-dimensional potential — (4Eρ2 + η2σ2a e0/ρ2).