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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.
6 citations
01 Jan 1988
TL;DR: In this paper, the changes of coordinates increasing the number of redundant variables are considered, and the Euler parameters, K-S variables, or other sets of variables by Broucke are discussed.
Abstract: Redundant variables have been successfully used in Celestial Mechanics for a long time. Here, we are concerned specially with the changes of coordinates increasing their number. Among them, the Euler parameters, K-S variables, or other sets of variables by Broucke are widely known.
6 citations
TL;DR: In this article, a simple construction of a group of birational canonical transformations of the fifth Painleve equation is given, which isomorphic to the affine Weyl group of the root system of type A3.
Abstract: The aim of this paper is to give a simple construction of a group of birational canonical transformations of the fifth Painleve equation isomorphic to the affine Weyl group of the root system of type A3 (Theorem 2 and Corollary 3). In previous works [6] (especially, §1) and [7], we constructed such groups of the sixth and the fourth equations by a method based on the synunetry of their Hamiltonian structures on their respective defining varieties with respect to Affine Weyl groups. To apply this method to the fifth equation, we reconstruct its defining variety to make clear the syrrunetry of the Hamiltonian structure on it Coming from the cyclic group of order four (Theorem 1). Prem this construction, we easily obtain generators of the desired group of birational canonical transformations without Okamoto's differential equation which is satisfied by a Hamiltonian auxiliary function ([3]). Our method clarifies the geometric meaning of birational canonical transformations of the fifth equation, and releases us from complicated calculation. AMS 1991 Subject Classification: 34A20, 34A26, 34A34. 1. Two polvnomial Hamiltonians According to Okamoto's theory of the isomonodromic deformation [2], each Painleve equation has its Hamiltonian structure, and is written in a Hamiltonian system with a polynomial Hamiltonian. For the fifth Pcdnleve equation, Okamoto [3] introduces a polynomial Hamiltonian K by the equation
6 citations
TL;DR: In this paper, a limited class of canonical transformations are introduced into the Lagrangian path integral method of quantization, and a simple example is given for path integral quantization in different representations.
Abstract: A limited class of canonical transformations is introduced into the Lagrangian path integral method of quantization. Path integral quantization in different representations is discussed and a simple example is given.
6 citations
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TL;DR: Plebanski as discussed by the authors showed that the coincidence of quantum cosmology solutions generated by solving a Euclidean version of the Hamilton-Jacobi equation for gravity and by using the complex canonical transformation of the Ashtekar variables is an artifact of the homogeneity of the cosmological space.
Abstract: The coincidence of quantum cosmology solutions generated by solving a Euclidean version of the Hamilton-Jacobi equation for gravity and by using the complex canonical transformation of the Ashtekar variables is discussed. An examination of similar solutions for the free electromagnetic field shows that this coincidence is an artifact of the homogeneity of the cosmological space. (This paper will appear in a festchrift volume for Jerzy Plebanski)
6 citations