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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 consistent, local coordinate formulation of covariant Hamiltonian field theory is presented, where the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, and the canonical transformation rules for fields are derived from generating functions.
Abstract: A consistent, local coordinate formulation of covariant Hamiltonian field theory is presented. While the covariant canonical field equations are equivalent to the Euler-Lagrange field equations, the covariant canonical transformation theory offers more general means for defining mappings that preserve the action functional - and hence the form of the field equations - than the usual Lagrangian description. Similar to the well-known canonical transformation theory of point dynamics, the canonical transformation rules for fields are derived from generating functions. As an interesting example, we work out the generating function of type F_2 of a general local U(N) gauge transformation and thus derive the most general form of a Hamiltonian density that is form-invariant under local U(N) gauge transformations.
10 citations
TL;DR: In this paper, a canonical transformation leading to the nonsecular part of time-independent perturbation calculus is proposed, which is used to derive expressions for effective Shen-Walls Hamiltonians, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations.
Abstract: A new method is proposed which involves a canonical transformation leading to the nonsecular part of time-independent perturbation calculus. The method is used to derive expressions for effective Shen-Walls Hamiltonians which, taken in the two-level approximation and on the inclusion of non-Hamiltonian terms into the dynamics of the system, lead to generalized Maxwell-Bloch equations. The rotating-wave approximation is written anew within the framework of our formalism.
10 citations
TL;DR: In this article, the duality transformation described by Arnol-d, which relates the orbits for different central potentials through a change of variables, is shown to be an example of a generalized canonical transformation, in an extended phase space that includes time as a dynamical variable.
Abstract: The duality transformation described by Arnol’d, which relates the orbits for different central potentials through a change of variables, is shown to be an example of a generalized canonical transformation, in an extended phase space that includes time as a dynamical variable.
10 citations
TL;DR: In this paper, a model distribution function for relativistic bi-Maxwellian with drift is proposed, based on the maximum entropy principle and the relativism canonical transformation, which is compatible with existing distribution functions and has a relatively simple form as well as smoothness.
Abstract: A model distribution function for relativistic bi-Maxwellian with drift is proposed, based on the maximum entropy principle and the relativistic canonical transformation. Since the obtained expression is compatible with the existing distribution functions and has a relatively simple form as well as smoothness, it might serve as a useful tool in the research fields of space or high temperature fusion plasmas.
10 citations
TL;DR: The present results demonstrate that the general real solutions may involve either exp, sin, cos, sinh or cosh under certain conditions depending on the type of the constants in the canonical transformation.
10 citations