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 published on a yearly basis
Papers
More filters
TL;DR: In this article, the canonical transformation of coordinates for a strong-coupled system of electron and phonon field was formulated for a bipolaron, taking into account the rigorous fulfillment of the conservation laws.
Abstract: The method of canonical transformation of coordinates is formulated for a strong-coupled system of electron and phonon field, taking into account the rigorous fulfillment of the conservation laws. The system of electronically excited terms of a bipolaron has been established. The sequence of the excited terms and their dependence on the distance between polarons have been obtained.
12 citations
TL;DR: In this paper, it was shown that the ADM-like transformation is canonical in extended phase space in a wide enough class of possible parametrizations for the full gravitational theory.
Abstract: A starting point for the present work was the statement recently discussed in the literature that two Hamiltonian formulations for the theory of gravity, the one proposed by Dirac and the other by Arnowitt - Deser - Misner, may not be related by a canonical transformation. In its turn, it raises a question about the equivalence of these two Hamiltonian formulations and their equivalence to the original formulation of General Relativity. We argue that, since the transformation from components of metric tensor to the ADM variables touches gauge degrees of freedom, which are non-canonical from the point of view of Dirac, the problem cannot be resolved in the limits of the Dirac approach. The proposed solution requires the extension of phase space by treating gauge degrees of freedom on an equal footing with other variables and introducing missing velocities into the Lagrangian by means of gauge conditions in differential form. We illustrate with a simple cosmological model the features of Hamiltonian dynamics in extended phase space. Then, we give a clear proof for the full gravitational theory that the ADM-like transformation is canonical in extended phase space in a wide enough class of possible parametrizations.
12 citations
TL;DR: In this paper, a canonical transformation of the cosmological phase space to write it in terms of a spinor was proposed, i.e., a pair of complex variables that transform under the fundamental representation of SU(1,1)∼SL(2,R).
Abstract: We build upon previous investigation of the one-dimensional conformal symmetry of the Friedman-Lemaitre-Robertson-Walker (FLRW) cosmology of a free scalar field and make it explicit through a reformulation of the theory at the classical level in terms of a manifestly SL(2,R)-invariant action principle. The new tool is a canonical transformation of the cosmological phase space to write it in terms of a spinor, i.e., a pair of complex variables that transform under the fundamental representation of SU(1,1)∼SL(2,R). The resulting FLRW Hamiltonian constraint is simply quadratic in the spinor and FLRW cosmology is written as a Schrodinger-like action principle. Conformal transformations can then be written as proper-time dependent SL(2,R) transformations. We conclude with possible generalizations of FLRW to arbitrary quadratic Hamiltonian and discuss the interpretation of the spinor as a gravitationally-dressed matter field or matter-dressed geometry observable.
12 citations
01 Jan 1991
TL;DR: For generic rational coadjoint orbits in the dual of the positive half of the loop algebra, the natural divisor coordinates associated to the eigenvector line bundles over the spectral curves project to Darboux coordinates on the Gl(r)-reduced space as discussed by the authors.
Abstract: For generic rational coadjoint orbits in the dual \(\tilde gl(r)^{ + *}\) of the positive half of the loop algebra \(\tilde gl(r)^{ + *}\), the natural divisor coordinates associated to the eigenvector line bundles over the spectral curves project to Darboux coordinates on the Gl(r)-reduced space. The geometry of the embedding of these curves in an ambient ruled surface suggests an intrinsic definition of symplectic structure on the space of pairs (spectral curves, duals of eigenvector line bundles) based on Serre duality. It is shown that this coincides with the reduced Kostant-Kirillov structure. For all Hamiltonians generating isospectral flows, these Darboux coordinates allow one to deduce a completely separated Liouville generating function, with the corresponding canonical transformation to linearizing variables identified as the Abel map.
12 citations
TL;DR: In this paper, a particle with a position-dependent mass in the context of a deformed algebraic structure (called κ-algebra), motivated by the Kappa-statistics, is presented.
Abstract: We present the quantum and classical mechanics formalisms for a particle with a position-dependent mass in the context of a deformed algebraic structure (named κ-algebra), motivated by the Kappa-statistics. From this structure, we obtain deformed versions of the position and momentum operators, which allow us to define a point canonical transformation that maps a particle with a constant mass in a deformed space into a particle with a position-dependent mass in the standard space. We illustrate the formalism with a particle confined in an infinite potential well and the Mathews–Lakshmanan oscillator, exhibiting uncertainty relations depending on the deformation.
12 citations