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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, the similarity of massive CSW scalar vertices and quark vertices can be understood using a kind of light-cone SUSY transformation presented in this paper.
Abstract: The similarity of massive CSW scalar vertices and quark vertices can be understood using a kind of light-cone SUSY transformation presented in this paper. We also show that the canonical transformation generating the MHV-SQCD Lagrangian, can be fixed by applying this light-cone SUSY transformation to the canonical transformation for MHV-QCD obtained in paper arxiv:0805.0239. Most of the massive CSW vertices for SQCD can also be pinned down in this way.

9 citations

Journal ArticleDOI
TL;DR: In this paper, exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation.
Abstract: Exact solutions of the Schrodinger equation are obtained for the Rosen-Morse and Scarf potentials with the position-dependent effective mass by appliying a general point canonical transformation. The general form of the point canonical transformation is introduced by using a free parameter. Two different forms of mass distributions are used. A set of the energy eigenvalues of the bound states and corresponding wave functions for target potentials are obtained as a function of the free parameter.

9 citations

Journal ArticleDOI
TL;DR: In this paper, the Mathieu transformation is defined by the solution of the Hori auxiliary system, which simplifies the algorithm since the inversion of the solution is no longer necessary.
Abstract: Any dynamical system can be put in generalized canonical form through the introduction of a set of auxiliary ‘conjugate’ variables or momenta and solved by perturbation theory based on Lie series. The application of Hori's method for generalized canonical system leads to a new canonical transformation — the Mathieu transformation — defined by the solution of the Hori auxiliary system. This new transformation simplifies the algorithm since the inversion of the solution of the Hori auxiliary system is no longer necessary. In this paper, we wish to show some peculiarities of this technique.

9 citations

Journal ArticleDOI
TL;DR: In this article, a new infinite-order perturbation approach for treating strongly anisotropic magnets was developed based on a canonical transformation of a given system into a new system with an effective two-ion anisotropy which can be treated by conventional spinwave techniques.
Abstract: We have developed a new infinite‐order perturbation approach for treating strongly anisotropic magnets. This formalism is based on a canonical transformation of a given system into a new system with an effective two‐ion anisotropy which, for example, can be treated by conventional spin‐wave techniques. An expression for the spin‐wave energy for the general conical magnetic moment configuration with arbitrary single‐ion anisotropy has been derived using this formalism. It was found that an analysis of the transverse spin‐wave spectra can at most result in a determination of a renormalized exchange integral and two renormalized anisotropy constants. A comparison of the theoretical predictions of this formalism with experimentally determined spin‐wave spectra indicate that a substantial part of the large two‐ion anisotropy, which had been previously introduced to describe the spin‐wave spectra in the heavy rare earth series, actually resulted from the fitting procedure which was used and not from any physica...

9 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the posterior probabilities of discriminant analysis are invariant under canonical transformation, and this result was used to justify the application of canonical variates for classification, thus integrating both approaches to discrimination.
Abstract: The usual computing procedures in discriminant analysis involve both classificatory and separatory functions (Geisser 1977). The first of these concerns classification of samples from a mixture of populations. Statistical assessment of classification procedures is based on rates of correct classification (Glick 1972,1973; Lachenbruch 1975; Michaelis 1973) or on the "loss" due to misclassification (Anderson 1958, Lachenbruch and Goldstein 1979). Separatory methods, on the other hand, deal with the transformation of data so that population differences are highlighted. This is done by means of "canonical variates," which define a subspace of reduced dimensionality wherein data often can be displayed to advantage. The canonical approach was first suggested by the work of Fisher (1936), and is closely associated with the multivariate analysis of variance (Anderson 1958, Rao 1965). Applied researchers often fail to recognize the statistical relationships between classificatory and separatory discrimination, in large part because mathematical forms, system dimensionalities, and even objectives differ between the two approaches. Kshirsagar and Arseven (1975) previously used a sample-based argument to show that full-rank canonical transforms can be used for classification. However, a key feature of the canonical analysis is the reduction of dimensionality. Thus it is important to know whether the same property holds for the reduced set of canonical variates. A simple matrix argument is used below to show that for certain distributions the posterior probabilities of discriminant analysis are invariant under canonical transformation. This result is used to justify the application of canonical variates for classification, thus integrating both approaches to discrimination.

9 citations


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