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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 paper, it was shown that the duality symmetry of type IIB superstring theory can be formulated as the canonical transformation interchanging momenta and magnetic degrees of freedom associated to the abelian world-volume gauge field of the D-3-brane.
Abstract: We show that the SL(2,R) duality symmetry of type IIB superstring theory can be formulated as the canonical transformation interchanging momenta and magnetic degrees of freedom associated to the abelian world-volume gauge field of the D-3-brane. D-strings are shown to be connected under the corresponding transformation in the world-sheet to the (m,n) family of string solutions of type IIB supergravity constructed by Schwarz. For the type IIA superstring the D-2-brane is mapped under the three dimensional world-volume electric-magnetic duality to the dimensional reduction of the membrane of M-theory.

22 citations

Journal ArticleDOI
TL;DR: In this article, the manifest form of the symmetry and the corresponding Noether identities are obtained in the first order formalism as well as in the Hamiltonian one, and it is proven that the symmetry can always be presented in the form of canonical transformation for the phase space variables.
Abstract: We study in the Hamiltonian framework the local transformations which leave invariant the Lagrangian action: δeS=div. Manifest form of the symmetry and the corresponding Noether identities is obtained in the first order formalism as well as in the Hamiltonian one. The identities have very simple form and interpretation in the Hamiltonian framework. Part of them allows one to express the symmetry generators which correspond to the primarily expressible velocities through the remaining one. The other part of the identities allows one to select subsystem of constraints with a special structure from the complete constraint system. It means, in particular, that the above written symmetry implies an appearance of the Hamiltonian constraints up to at least ([k]+1) stage. It is proven also that the Hamiltonian symmetries can always be presented in the form of canonical transformation for the phase space variables. The manifest form of the resulting generating function is obtained.

22 citations

Journal ArticleDOI
TL;DR: In this article, a canonical transformation to new action-angle variables (J,Ψ) is constructed by fitting surfaces to computed orbits, which leads to an accurate map of resonant tune lines into J space, which serves to locate dangerous regions of phase space.

22 citations

Journal ArticleDOI
TL;DR: In this paper, the quantization of two analogous one-degree-of-freedom Hamiltonian systems is discussed, and the outcome is analogous, if perhaps even more clear cut, than in the previous three cases; it also confirms that different quantized spectra may be obtained if quantization is performed before or after a (nonlinear) canonical transformation.
Abstract: In two previous papers the quantization was discussed of three one-degree-of-freedom Hamiltonians featuring a constant c, the value of which does not influence at all the corresponding classical dynamics (which is characterized by isochronous solutions, all of them periodic with period 2π: “nonlinear harmonic oscillators”), but turned instead out to influence, possibly quite nontrivially, the results in the quantized case. The quantization of two analogous Hamiltonian systems is discussed in this paper. The outcome is analogous, if perhaps even more clear cut, than in the previous three cases; it also confirms that different quantized spectra may be obtained if quantization is performed before or after a (nonlinear) canonical transformation.

22 citations

Journal ArticleDOI
TL;DR: In this paper, a systematic method is presented for the construction of invariants for the damped oscillator under the action of a driving force and for the N-dimensional isotropic or anisotropic oscillator.
Abstract: A systematic method is presented for the construction of invariants for the damped oscillator under the action of a driving force and for the N‐dimensional isotropic or anisotropic oscillator. Invariants for time‐dependent oscillators are obtained by canonical transformation. The treatment holds in both classical and quantum mechanics.

22 citations


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