Topic
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, it was shown that the problem of a free eletron in a uniform magnetic field provides an interesting example for the use of recently developed canonical transformation methods in quantum mechanics, and the Schrodinger equation is immediately solved by a unitary transformation corresponding to a finite linear symplectic transformation in phase space.
Abstract: It is shown that the problem of a free eletron in a uniform magnetic field provides an interesting example for the use of recently developed canonical transformation methods in quantum mechanics. The Schrodinger equation is immediately solved by a unitary transformation corresponding to a finite linear symplectic transformation in phase space. The natural invariance and dynamical groups involve affine and not only linear symplectic transformations, and the Weyl group turns out to be an appropriate invariance group to account completely for the infinite degeneracies.
40 citations
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TL;DR: In this paper, the canonical formalism of a singular-Lagrangian model describing the interaction between two relativistic particles is studied and the covariance and quantization of the model are discussed.
Abstract: The canonical formalism of a singular-Lagrangian model describing the interaction between two relativistic particles is studied. Instead of following the Dirac method, we make use of a canonical transformation that enables us to work in the complete phase space. The covariance and the quantization of the model are discussed.
40 citations
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TL;DR: Exact operator quantization is performed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to the one proposed by Callan, Giddings, Harvey, and Strominger, in the special case with 24 massless matter scalars.
Abstract: Exact operator quantization is performed of a model of two-dimensional dilaton gravity in Lorentzian spacetime, classically equivalent to the one proposed by Callan, Giddings, Harvey, and Strominger, in the special case with 24 massless matter scalars. This is accomplished by developing a nonlinear and nonlocal quantum canonical transformation of basic interacting fields into a set of free fields, rigorously taking into account the spatially closed boundary condition. The quantized model enjoys conformal invariance and the entire set of physical states and operators are obtained in the BRST formalism. In addition, a rather detailed discussion of the nature of the basic issues for exact treatment of models of quantum gravity is provided
40 citations
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TL;DR: In this article, it was shown that an explicit canonical Runge-Kutta-Nystrom method is canonical if and only its adjoint is explicit, where the adjoint of a method is obtained by time reversal.
Abstract: Canonical Runge–Kutta–Nystrom methods for Hamiltonian dynamical systems are considered. These systems arise in various areas in the physical sciences. Canonical methods preserve certain properties of the system. In this paper, it is shown that an explicit Runge–Kutta–Nystrom method is canonical if and only its adjoint is explicit. The adjoint of a method is obtained by time reversal. One application for this result and other results in this paper is that if an explicit canonical Runge–Kutta–Nystrom method of odd order is concatenated with its adjoint the result is an explicit canonical method of one order higher.
39 citations
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TL;DR: In this article, it was shown that the string worldsheet theory of Gaiotto-Maldacena holographic duals generically fails to be classically integrable.
Abstract: We show that the string worldsheet theory of Gaiotto-Maldacena holographic duals to $$ \mathcal{N}=2 $$
superconformal field theories generically fails to be classically integrable. We demonstrate numerically that the dynamics of a winding string configuration possesses a non-vanishing Lyapunov exponent. Furthermore an analytic study of the Normal Variational Equation fails to yield a Liouvillian solution. An exception to the generic non-integrability of such backgrounds is provided by the non-Abelian T-dual of AdS5 × S5; here by virtue of the canonical transformation nature of the T-duality classical integrability is known to be present.
39 citations