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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, it was shown that the background-quantum splitting of SU(N) Yang-Mills theory is non-trivially deformed at the quantum level by a canonical transformation with respect to the Batalin-Vilkovisky bracket associated with the Slavnov-Taylor identity.
Abstract: We show that for a SU(N) Yang-Mills theory the classical background-quantum splitting is non-trivially deformed at the quantum level by a canonical transformation with respect to the Batalin-Vilkovisky bracket associated with the Slavnov-Taylor identity of the theory. This canonical transformation acts on all the fields (including the ghosts) and antifields; it uniquely fixes the dependence on the background field of all the one-particle irreducible Green's functions of the theory at hand. The approach is valid both at the perturbative and non-perturbative level, being based solely on symmetry requirements. As a practical application, we derive the renormalization group equation in the presence of a generic background and apply it in the case of a SU(2) instanton. Finally, we explicitly calculate the one-loop deformation of the background-quantum splitting in lowest order in the instanton background.
18 citations
TL;DR: In this paper, a unified treatment of the analytical bound of the Schr€ equation for exponential-type potentials in D-dimensions is proposed, and the energy spectra and wavefunctions are derived straightforward from the proposed approach.
Abstract: In this article, using an exactly-solvable multiparameter exponential-type potential we propose a unified treatment of the analytical bound—state solutions of the Schr€ equation for exponential-type potentials in D-dimensions. Our proposal accepts different approximations to the centrifugal term; however, its usefulness is exemplified in the frame of the Green and Aldrich approach. This fact enables us to compare our results with specific potentials found in the literature and that are obtained here as particular cases of our proposal. That is, instead of solving a specific exponential-type potential, by resorting each time to a specialized method, the energy spectra and wavefunctions are derived straightforward from the proposed approach. Furthermore, our proposal can be used as an alternative way in the search of solutions to new exponentialtype potentials besides that one can study different approximations to the term 1=r 2 . V C 2014 Wiley Periodicals, Inc.
18 citations
TL;DR: In this article, the authors propose a Hamiltonian model for gravity waves on the surface of a fluid layer surrounding a gravitating sphere, which can be used as a starting point for simpler models, derived systematically by expanding the Hamiltonian in dimensionless parameters.
Abstract: We propose a Hamiltonian model for gravity waves on the surface of a fluid layer surrounding a gravitating sphere. The general equations of motion are nonlocal and can be used as a starting point for simpler models, which can be derived systematically by expanding the Hamiltonian in dimensionless parameters. In this paper, we focus on the small wave amplitude regime. The first-order nonlinear terms can be eliminated by a formal canonical transformation. Similarly, many of the second order terms can be eliminated. The resulting model has the feature that it leaves invariant several finite-dimensional subspaces on which the motion is integrable.
18 citations
TL;DR: In this paper, a new symplectic variational approach is developed for modeling dissipation in kinetic equations, which yields a double bracket structure in phase space which generates kinetic equations representing coadjoint motion under canonical transformations.
18 citations
TL;DR: In this paper, it was shown that the Hamiltonian of the first-order formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters.
Abstract: It is shown that the Hamiltonian of the Einstein affine-metric (first-order) formulation of General Relativity (GR) leads to a constraint structure that allows the restoration of its unique gauge invariance, four-diffeomorphism, without the need of any field dependent redefinition of gauge parameters as in the case of the second-order formulation. In the second-order formulation of ADM gravity the need for such a redefinition is the result of the non-canonical change of variables (arXiv:0809.0097). For the first-order formulation, the necessity of such a redefinition “to correspond to diffeomorphism invariance” (reported by Ghalati, arXiv:0901.3344) is just an artifact of using the Henneaux–Teitelboim–Zanelli ansatz (Nucl. Phys. B 332:169, 1990), which is sensitive to the choice of linear combination of tertiary constraints. This ansatz cannot be used as an algorithm for finding a gauge invariance, which is a unique property of a physical system, and it should not be affected by different choices of linear combinations of non-primary first class constraints. The algorithm of Castellani (Ann. Phys. 143:357, 1982) is free from such a deficiency and it leads directly to four-diffeomorphism invariance for first, as well as for second-order Hamiltonian formulations of GR. The distinct role of primary first class constraints, the effect of considering different linear combinations of constraints, the canonical transformations of phase-space variables, and their interplay are discussed in some detail for Hamiltonians of the second- and first-order formulations of metric GR. The first-order formulation of Einstein–Cartan theory, which is the classical background of Loop Quantum Gravity, is also discussed.
18 citations