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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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Journal ArticleDOI
TL;DR: In this article, the Hamiltonian thermodynamics formalism is applied to the general d-dimensional Reissner-Nordstroem-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology.
Abstract: The Hamiltonian thermodynamics formalism is applied to the general d-dimensional Reissner-Nordstroem-anti-de Sitter black hole with spherical, planar, and hyperbolic horizon topology. After writing its action and performing a Legendre transformation, surface terms are added in order to guarantee a well-defined variational principle with which to obtain sensible equations of motion, and also to allow later on the thermodynamical analysis. Then a Kuchar canonical transformation is done, which changes from the metric canonical coordinates to the physical parameters coordinates. Again, a well-defined variational principle is guaranteed through boundary terms. These terms influence the falloff conditions of the variables and at the same time the form of the new Lagrange multipliers. Reduction to the true degrees of freedom is performed, which are the conserved mass and charge of the black hole. Upon quantization a Lorentzian partition function Z is written for the grand canonical ensemble, where the temperature T and the electric potential {phi} are fixed at infinity. After imposing Euclidean boundary conditions on the partition function, the respective effective action I{sub *}, and thus the thermodynamical partition function, is determined for any dimension d and topology k. This is a quite general action. Several previous results can be then condensed inmore » our single general formula for the effective action I{sub *}. Phase transitions are studied for the spherical case, and it is shown that all the other topologies have no phase transitions. A parallel with the Bose-Einstein condensation can be established. Finally, the expected values of energy, charge, and entropy are determined for the black hole solution.« less

21 citations

Journal ArticleDOI
TL;DR: In this article, a canonical transformation of the single-particle Hamiltonian is proposed to eliminate those interaction terms which are linear in the fields, and the new entity (the "oscillation centre") then has no first-order jittering motion, and generalized ponderomotive forces appear as nonlinear terms in the transformed Hamiltonian.
Abstract: A novel approach to the theory of nonlinear mode coupling in hot magnetized plasma is presented. The formulation retains the conceptual simplicity of the familiar ponderomotive-scalar-potential method, but removes the approximations. The essence of the approach is a canonical transformation of the single-particle Hamiltonian, designed to eliminate those interaction terms which are linear in the fields. The new entity (the 'oscillation centre') then has no first-order jittering motion, and generalized ponderomotive forces appear as nonlinear terms in the transformed Hamiltonian. This viewpoint is applied to derive a compact symmetric formula for the general three-wave coupling coefficient in hot uniform magnetized plasma, and to extend the conventional ponderomotive-scalar-potential method to the domain of strongly magnetized plasma.

21 citations

Book ChapterDOI
TL;DR: In this paper, three suggestions are made for breaking the gridlock which paralyses progress in automating massive symbolic calculations in celestial mechanics: simplifications by canonical transformations, object oriented programming to endow the algebra of Poisson series with various structures and massively parallel processing.
Abstract: Three suggestions are made for breaking the gridlock which paralyses progress in automating massive symbolic calculations in celestial mechanics:(i) simplifications by canonical transformations, (ii) object oriented programming to endow the algebra of Poisson series with various structures, (iii) massively parallel processing.

21 citations

Posted Content
TL;DR: In this article, the classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) Hamiltonians.
Abstract: The classical and quantum mechanical correspondence for constant mass settings is used, along with some point canonical transformation, to find the position-dependent mass (PDM) classical and quantum Hamiltonians. The comparison between the resulting quantum PDM-Hamiltonian and the von Roos PDM-Hamiltonian implied that the ordering ambiguity parameters of von Roos are strictly determined. Eliminating, in effect, the ordering ambiguity associated with the von Roos PDM-Hamiltonian. This, consequently, played a vital role in the construction and identification of the PDM-momentum operator. The same recipe is followed to identify the form of the minimal coupling of electromagnetic interactions for the classical and quantum PDM-Hamiltonians. It turned out that whilst the minimal coupling may very well inherit the usual form in classical mechanics, it admits a necessarily different and vital form in quantum mechanics. Under our point transformation settings, only one of the two commonly used vector potentialsis found eligible and is considered for our Illustrative examples.

21 citations

Journal ArticleDOI
TL;DR: In this paper, a procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed.
Abstract: A procedure which obviates the constraint imposed by the conflict between consistent quantization and the invariance of the Hamiltonian description under nonlinear canonical transformation is proposed. This new quantization scheme preserves the Noether point symmetries of the underlying Lagrangian in order to construct the Schrodinger equation. Two examples are given, one known and one new: the quantization of a charged particle in a uniform magnetic field in the plane, and that of the ‘goldfish’ many-body problem extensively studied by Calogero et al.

21 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202218
202158
202042
201932
201829