Canonical transformation

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

Some Generalizations of the Foldy-Wouthuysen Transformation

Abstract: A canonical transformation similar to that given by Foldy and Wouthuysen is obtained for the spin zero and one theories. For free particles positive and negative charge states are separately described by one or three component wave functions. It is found that the resulting forms for operators and the non-relativistic limits are quite similar to that for spin \textonehalf{}. The resulting similarity is found to carry over to still higher spins. Particles moving in magnetic fields are described most simply using the transformed representation.

Actions for Gravity, with Generalizations: A Review

Abstract: Related to the classical Ashtekar Hamiltonian, there have been discoveries regarding new classical actions for gravity in (2+1)- and (3+1)-dimensions, and also generalizations of Einstein's theory of gravity. In this review, I will try to clarify the relations between the new and old actions for gravity, and also give a short introduction to the new generalizations. The new results/treatments in this review are: 1. A more detailed constraint analysis of the Hamiltonian formulation of the Hilbert- Palatini Lagrangian in (3+1)-dimensions. 2. The canonical transformation relating the Ashtekar- and the ADM-Hamiltonian in (2+1)-dimensions is given. 3. There is a discussion regarding the possibility of finding a higher dimensional Ashtekar formulation. There are also two clarifying figures (in the beginning of chapter 2 and 3, respectively) showing the relations between different action-formulations for Einstein gravity in (2+1)- and (3+1)-dimensions.

Canonical Forms for Symplectic and Hamiltonian Matrices

Abstract: This paper gives a constructive method for finding canonical forms for symplectic and Hamiltonian matrices. No restrictions are made on the eigen values or their multiplicity. Real canonical forms are treated in detail.

Currents, charges, and canonical structure of pseudodual chiral models.

Abstract: We discuss the pseudodual chiral model to illustrate a class of two-dimensional theories which have an infinite number of conservation laws but allow particle production, at variance with naive expectations. We describe the symmetries of the pseudodual model, both local and nonlocal, as transmutations of the symmetries of the usual chiral model. We refine the conventional algorithm to more efficiently produce the nonlocal symmetries of the model, and we discuss the complete local current algebra for the pseudodual theory. We also exhibit the canonical transformation which connects the usual chiral model to its fully equivalent dual, further distinguishing the pseudodual theory.

Duality system in applied mechanics and optimal control

Abstract: Contents Preface Introduction 0.1. Introduction to Precise integration method 1: Introduction to analytical dynamics 1.1. Holonomic and nonholonomic constraints 1.2. Generalized displacement, degrees of freedom and virtual displacement 1.3. Principle of virtual displacement and the D'Alembert principle 1.4. Lagrange equation 1.5. Hamilton variational principle 1.6. Hamiltonian canonical equations 1.7. Canonical transformation 1.8. Symplectic description of the canonical transformation 1.9. Poisson bracket 1.10. Action 1.11. Hamilton-Jacobi equation 2: Vibration theory 2.1. Single degree of freedom vibration 2.2. Vibration of multi-degrees of freedom system 2.3. Small vibration of gyroscopic systems 2.4. Non-linear vibration of multi-degrees of freedom system 2.5. Discussion on the stability of gyroscopic system 3: Probability and stochastic process 3.1. Preliminary of probability theory 3.2. Preliminary of stochastic process 3.3. Quadratic moment stochastic process (regular process) 3.4. Normal stochastic process 3.5. Markoff process 3.6. Spectral density of stationary stochastic process 4: Random vibration of structures 4.1. Models of random excitation 4.2. Response of structures under stationary excitations 4.3. Response under excitation of non-stationary stochastic process 5: Elastic system with single continuous coordinate 5.1. Fundamental equations of Timoshenco beam theory 5.2. Potential energy density and mixed energy density 5.3. Separation of variables, Adjoint symplectic ortho-normality 5.4. Multiple eigenvalues and the Jordan normal form 5.5. Expansion solution of the inhomogeneous equation 5.6. Two end boundary conditions 5.7. Interval mixed energy and precise integration method 5.8. Eigenvector based solution of Riccati equations 5.9. Stepwise integrationmethod by means of sub-structural combination 5.10. Influence function of single continuous coordinate system 5.11. Power flow 5.12. Wave scattering analysis 5.13. Wave induced resonance 5.14. Wave propagation along periodical structures 6: Linear optimal control, theory and computation 6.1. State space of linear system 6.2. Theory of stability 6.3. Prediction, filtering and smoothing 6.4. Prediction and its computation 6.5. Kalman filter 6.6. Optimal smoothing and computations 6.7. Optimal control 6.8. Robust control Concluding remarks