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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, the Dirac theory of quantization under constraints is used to obtain an effective Hamiltonian for N solitons which reduces, in the one-soliton case, to that of Gervais and Sakita.
30 citations
TL;DR: In this paper, the canonical formalism for constrained systems with a finite number of degrees of freedom was developed by making use of the Poincare-Cartan integral invariant method.
Abstract: In this work we develop the canonical formalism for constrained systems with a finite number of degrees of freedom by making use of the Poincare–Cartan integral invariant method. A set of variables suitable for the reduction to the physical ones can be obtained by means of a canonical transformation. From the invariance of the Poincare–Cartan integral under canonical transformations we get the form of the equations of motion for the physical variables of the system.
30 citations
TL;DR: A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways.
Abstract: A canonical transformation which relates the model of a massive relativistic particle moving near the horizon of an extremal black hole in four dimensions and the conventional conformal mechanics is constructed in two different ways. The first approach makes use of the action-angle variables in the angular sector. The second scheme relies upon integrability of the system in the sense of Liouville.
30 citations
01 Aug 1982
TL;DR: In this paper, a proof of the gauge-invariant renormalizability of general gauge theories in arbitrary gauges is given, and it is shown that a canonical change of variables in the initial effective action also generates only a canonical transformation of variable in the renormalized action and in the vertex generating functional.
Abstract: A proof is given of the gauge-invariant renormalizability of general gauge theories in arbitrary gauges. We show that a canonical change of variables in the initial effective action also generates only a canonical change of variables in the renormalized action and in the vertex generating functional. We note that the gauge condition enters into the effective action as a canonical transformation. As a consequence, changing the gauge condition is equivalent to a canonical transformation of the renormalized action and the vertex generating functional. This, in turn, implies the gauge invariance of the renormalized S matrix.
30 citations
TL;DR: In this paper, the authors consider the problem of a deformed oscillator in both classical and quantum formalisms, and compare the results of the problem through the principle of correspondence and the WKB approximation.
Abstract: We consider canonically conjugated generalized space and linear momentum operators $\hat{x}_q$ and $ \hat{p}_q$ in quantum mechanics, associated to a generalized translation operator which produces infinitesimal deformed displacements controlled by a deformation parameter $q$. A canonical transformation $(\hat{x}, \hat{p}) \rightarrow (\hat{x}_q, \hat{p}_q)$ leads the Hamiltonian of a position-dependent mass particle in usual space to another Hamiltonian of a particle with constant mass in a conservative force field of the deformed space. The equation of motion for the classical phase space $(x, p)$ may be expressed in terms of the deformed (dual) $q$-derivative. We revisit the problem of a $q$-deformed oscillator in both classical and quantum formalisms. Particularly, this canonical transformation leads a particle with position-dependent mass in a harmonic potential to a particle with constant mass in a Morse potential. The trajectories in phase spaces $(x,p)$ and $(x_q, p_q)$ are analyzed for different values of the deformation parameter. Lastly, we compare the results of the problem in classical and quantum formalisms through the principle of correspondence and the WKB approximation.
29 citations