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Canonical transformation
About: Canonical transformation is a research topic. Over the lifetime, 1854 publications have been published within this topic receiving 38019 citations.
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TL;DR: In this article, a model which describes a relativistic interaction between two point particles via an action at a distance is derived from a set of hypotheses on the relativism dynamics.
Abstract: In this paper a model which describes a relativistic interaction between two point particles via an action at a distance is derived from a set of hypotheses on the relativistic dynamics. From this set of hypotheses a singular Lagrangian is obtained. The aim of this paper is to find a link between the singular-Lagrangian approach and other approaches to the relativistic dynamics of two particles. The connection of this Lagrangian model with the predictive approach of the relativistic mechanics is studied, by showing that it is possible to calculate the instantaneous forces, at least in principle. An explicit canonical transformation is given, such that a subset of the new canonical variables becomes free of constraints. In this way the instant form of the relativistic dynamics found by Bakamjan and Thomas and by Foldy is recovered.
15 citations
TL;DR: In this paper, it was shown that for a generalization to systems invariant under non-conventional time reversal, which also belong to the orthogonal symmetry class, it is necessary to redefine the configuration space by a suitable canonical transformation.
Abstract: Recently, Sieber and Richter calculated semiclassically a first off-diagonal contribution to the orthogonal form factor for a billiard on a surface of constant negative curvature. Following prior suggestions from the theory of disordered systems, they considered orbit pairs with almost the same action. For a generalization to systems invariant under non-conventional time reversal, which also belong to the orthogonal symmetry class, we show here that it is necessary to redefine the configuration space by a suitable canonical transformation; the distinction of this space is that it lets time reversal look conventional.
15 citations
TL;DR: In this paper, the motion of two massive particles is considered within the framework of the first post-Newtonian approximation, and the system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables.
Abstract: The motion of two massive particles is considered within the framework of the first post-Newtonian approximation. The system Hamiltonian is constructed and normalized through first order using a canonical transformation method of implicit variables. Closed-form solutions for the Delaunay elements in the phase space are obtained. The bridge between the phase space and the state space of the Lagrangian of the motion is provided by a velocity-dependent Legendre transformation. By explicit inversion of this transformation, expressions for the Keplerian elements in the state space are obtained from the Delaunay element solutions.
15 citations
TL;DR: In this paper, a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals was developed, which is based on a mapping of the nonlinear response of the "bare" system onto the linear response of a "dressed" system, characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials.
Abstract: We develop a theory describing the effects of many-particle Coulomb correlations on the coherent ultrafast nonlinear optical response of semiconductors and metals. Our approach is based on a mapping of the nonlinear optical response of the "bare" system onto the linear response of a "dressed" system. The latter is characterized by effective time-dependent optical transition matrix elements, electron/hole dispersions, and interaction potentials, which in undoped semiconductors are determined by the single-exciton and two-exciton Green functions in the absence of optical fields. This mapping is achieved by eliminating the optically-induced charge fluctuations from the Hamiltonian using a Van Vleck canonical transformation. It takes into account all many-body contributions up to a given order in the optical fields as well as important Coulomb-induced quantum dynamics to all orders in the optical field. Our approach allows us to distinguish between optical nonlinearities of different origins and provides a physically-intuitive interpretation of their manifestations in ultrafast coherent nonlinear optical spectroscopy.
15 citations
TL;DR: First, the normal form in the vicinity of the stationary solution of the autonomous Hamiltonian system is recalled, then normal forms of Hamiltonians of nonlinear periodic systems are found and a feature of the real case in the situation of parametric resonance is discovered.
Abstract: First, the normal form in the vicinity of the stationary solution of the autonomous Hamiltonian system is recalled. Next, linear periodic Hamiltonian systems are considered. For them, normal forms of the Hamiltonians in the complex and real cases are found. A feature of the real case in the situation of parametric resonance is discovered. Next, normal forms of Hamiltonians of nonlinear periodic systems are found. Using an additional canonical transformation, such a normal form can be always reduced to an autonomous Hamiltonian system that preserves all small parameters and symmetries of the original system. The local families of fixed points of this autonomous system are associated with families of periodic solutions to the original system. A similar theory is constructed in the neighborhood of the periodic solution to the autonomous system. All transformations are algorithmic and can be implemented in a computer algebra system.
15 citations