scispace - formally typeset
Search or ask a question
Topic

Canonical transformation

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


Papers
More filters
Journal ArticleDOI
TL;DR: In this paper, a generalized master equation (GME) approach for carriers interacting with phonons by a local linear coupling is applied to the time-convolutionless GME approach for a single-particle density matrix, which is shown to yield a loss of coherence of carrier propagation with increasing time as well as a proper asymptotic state at any temperature.
Abstract: A trick permitting to apply generalized master equation (GME) theory together with canonical transformation but quantities of interest (single-particle density matrix) remaining untransformed is applied to the time-convolutionless GME approach for carriers interacting with phonons by a local linear coupling. In contrast with time convolution theories (Mori, time-convolution GME), it is found that the second-order perturbational approach in the above coupling is already able to yield a loss of coherence of carrier propagation with increasing time as well as a proper asymptotic state at any temperature. Moreover, dependence on the degree of the initial polaron cloud formation is shown, as expected but again in contrast with the above theories, to disappear explicitly after a short period of the polaron cloud reconstruction from equations determining the time development of the single-particle density matrix. A prediction on the Weber effect and charge-carrier generation process in narrow band materials is given. Correspondence with a recent generalization of the Haken-Strobl-Reineker model is found.

6 citations

Journal ArticleDOI
TL;DR: In this paper, the authors applied the canonical transformation to pseudo-scalar meson theory with pseudoscalar coupling and showed that the resulting Hamiltonian shows a good tendency to account for the S.phase shifts for the nucleon 1t-meson scattering.
Abstract: The method of canonical transformation is applied to the pseudo-scalar meson theory with pseudoscalar coupling. It will be shown that tbe Tanj1)-Foldy~) transformation results as the best one when regarded as a variational function among the similar family of transformation. The resulting Hamiltonian was ordered assuming some cut-off for the virtual meson momentum, and performing the mass renormalization. This Hamiltonian shows a good tendency to account for the S.phase shifts for the nucleon 1t-meson scattering; the L-S coupling (or· q; X 1t) in the isotopic spin space, which is positive for the T=3/2 state and negative for the T=I/2 state, becomes rwice as large as obtained by the perturbation theory.

6 citations

Posted Content
TL;DR: In this article, the authors re-examine the analysis of this model and find that it does not support the author's conclusion and argue that the conclusion, ''we cannot consider the Dirac approach as fundamental and undoubted', made in the paper by Shestakova (Class. 28 055009, 2011), is based upon an incomplete and flawed analysis of the simple model presented in section 3 of the article.
Abstract: We argue that the conclusion, `we cannot consider the Dirac approach as fundamental and undoubted', made in the paper by Shestakova (Class. Quantum Grav. 28 055009, 2011), is based upon an incomplete and flawed analysis of the simple model presented in section 3 of the article. We re-examine the analysis of this model and find that it does not support the author's conclusion. For the theory of gravity neither the equivalence of the effective action nor its Hamiltonian formulation is given by the author, therefore, we only provide a brief commentary.

6 citations

Posted Content
TL;DR: In this article, a soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method, where the solutions are associated with the collective excitation of the electron-positron field, and the canonical transformation of the variables allowed to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.
Abstract: A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.

6 citations

Journal ArticleDOI
TL;DR: In this article, it was shown that Egorov's theorem on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators can be sharpened.
Abstract: We prove that the theorem of Egorov, on the canonical transformation of symbols of pseudodifferential operators conjugated by Fourier integral operators, can be sharpened. The main result is that the statement of Egorov's theorem remains true if, instead of just considering the principal symbols in $S^m/S^{m-1}$ for the pseudodifferential operators, one uses refined principal symbols in $S^m/S^{m-2}$, which for classical operators correspond simply to the principal plus the subprincipal symbol, and can generally be regarded as the first two terms of its Weyl symbol expansion: we call it the principal Weyl symbol of the pseudodifferential operator. Particular unitary Fourier integral operators, associated to the graph of the canonical transformation, have to be used in the conjugation for the higher accuracy to hold, leading to microlocal representations by oscillatory integrals with specific symbols that are given explicitly in terms of the generating function that locally describes the graph of the transformation. The motivation for the result is based on the optimal symplectic invariance properties of the Weyl correspondence in ${\mathbb R}^n$ and its symmetry for real symbols.

6 citations


Network Information
Related Topics (5)
Differential equation
88K papers, 2M citations
84% related
Ground state
70K papers, 1.5M citations
83% related
Boundary value problem
145.3K papers, 2.7M citations
83% related
Field (physics)
95K papers, 1.5M citations
82% related
Matrix (mathematics)
105.5K papers, 1.9M citations
82% related
Performance
Metrics
No. of papers in the topic in previous years
YearPapers
20237
202218
202158
202042
201932
201829