Relevant bibliographies by topics / Poisson brackets

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Poisson brackets'

Author: Grafiati
Published: 4 June 2021
Last updated: 14 March 2023

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Journal articles on the topic "Poisson brackets"

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KAHNG, BYUNG-JAY. "DEFORMATION QUANTIZATION OF CERTAIN NONLINEAR POISSON STRUCTURES." International Journal of Mathematics 09, no. 05 (August 1998): 599–621. http://dx.doi.org/10.1142/s0129167x98000269.

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As a generalization of the linear Poisson bracket on the dual space of a Lie algebra, we introduce certain nonlinear Poisson brackets which are "cocycle perturbations" of the linear Poisson bracket. We show that these special Poisson brackets are equivalent to Poisson brackets of central extension type, which resemble the central extensions of an ordinary Lie bracket via Lie algebra cocycles. We are able to formulate (strict) deformation quantizations of these Poisson brackets by means of twisted group C*-algebras. We also indicate that these deformation quantizations can be used to construct some specific non-compact quantum groups.
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BATALIN, IGOR, and ROBERT MARNELIUS. "DUALITIES BETWEEN POISSON BRACKETS AND ANTIBRACKETS." International Journal of Modern Physics A 14, no. 32 (December 30, 1999): 5049–73. http://dx.doi.org/10.1142/s0217751x99002384.

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Recently it has been shown that antibrackets may be expressed in terms of Poisson brackets and vice versa for commuting functions in the original bracket. Here we also introduce generalized brackets involving higher antibrackets or higher Poisson brackets where the latter are of a new type. We give generating functions for these brackets for functions in arbitrary involutions in the original bracket. We also give master equations for generalized Maurer–Cartan equations. The presentation is completely symmetric with respect to Poisson brackets and antibrackets.
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Bruce, Andrew James. "Odd Jacobi Manifolds and Loday-Poisson Brackets." Journal of Mathematics 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/630749.

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We construct a nonskew symmetric version of a Poisson bracket on the algebra of smooth functions on an odd Jacobi supermanifold. We refer to such Poisson-like brackets as Loday-Poisson brackets. We examine the relations between the Hamiltonian vector fields with respect to both the odd Jacobi structure and the Loday-Poisson structure. Furthermore, we show that the Loday-Poisson bracket satisfies the Leibniz rule over the noncommutative product derived from the homological vector field.
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De Sole, Alberto, Victor G. Kac, Daniele Valeri, and Minoru Wakimoto. "Poisson Λ-brackets for Differential–Difference Equations." International Mathematics Research Notices 2020, no. 13 (October 30, 2018): 4144–90. http://dx.doi.org/10.1093/imrn/rny242.

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Abstract We introduce the notion of a multiplicative Poisson $\lambda$-bracket, which plays the same role in the theory of Hamiltonian differential–difference equations as the usual Poisson $\lambda$-bracket plays in the theory of Hamiltonian partial differential equations (PDE). We classify multiplicative Poisson $\lambda$-brackets in one difference variable up to order 5. As an example, we demonstrate how to apply the Lenard–Magri scheme to a compatible pair of multiplicative Poisson $\lambda$-brackets of order 1 and 2, to establish integrability of the Volterra chain.
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FERGUSON, JAMES T. "SECOND-ORDER DEFORMATIONS OF HYDRODYNAMIC-TYPE POISSON BRACKETS." Glasgow Mathematical Journal 51, A (February 2009): 75–82. http://dx.doi.org/10.1017/s0017089508004795.

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AbstractThis paper is concerned with the properties of differential-geometric-type Poisson brackets specified by a differential operator of degree 2. It also considers the conditions required for such a Poisson bracket to form a bi-Hamiltonian structure with a hydrodynamic-type Poisson bracket.
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Chen, K. C. "Constructing Poisson and Dissipative Brackets of Mixtures by using Lagrangian-to-Eulerian Transformation." Journal of Mechanics 26, no. 2 (June 2010): 219–28. http://dx.doi.org/10.1017/s1727719100003075.

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AbstractThis paper aims to construct the bracket formalism of mixture continua by using the method of Lagrangian- to-Eulerian (LE) transformation. The LE approach first builds up the transformation relations between the Eulerian state variables and the Lagrangian canonical variables, and then transforms the bracket in Lagrangian form to the bracket in Eulerian form. For the conservative part of the bracket formalism, this study systematically generates the noncanonical Poisson brackets of a two-component mixture. For the dissipative part, we deduce the Eulerian-variable-based dissipative brackets for viscous and diffusive mechanisms from their Lagrangian-variable-based counterparts. Finally, the evolution equations of a micromorphic fluid, which can be treated as a multi-component mixture, are derived by constructing its Poisson and dissipative brackets.
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Bimonte, G., G. Esposito, G. Marmo, and C. Stornaiolo. "Peierls Brackets in Field Theory." International Journal of Modern Physics A 18, no. 12 (May 10, 2003): 2033–39. http://dx.doi.org/10.1142/s0217751x03015453.

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Peierls brackets are part of the space-time approach to quantum field theory, and provide a Poisson bracket which, being defined for pairs of observables which are group invariant, is group invariant by construction. It is therefore well suited for combining the use of Poisson brackets and the full diffeomorphism group in general relativity. The present paper provides an introduction to the topic, with applications to gauge field theory.
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Guttenberg, S. "Derived Brackets from Super-Poisson Brackets." Nuclear Physics B - Proceedings Supplements 171 (September 2007): 279–80. http://dx.doi.org/10.1016/j.nuclphysbps.2007.06.025.

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Beltiţă, Daniel, Tomasz Goliński, and Alice-Barbara Tumpach. "Queer Poisson brackets." Journal of Geometry and Physics 132 (October 2018): 358–62. http://dx.doi.org/10.1016/j.geomphys.2018.06.013.

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Eastwood, M., and G. Marí Beffa. "Geometric Poisson brackets on Grassmannians and conformal spheres." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 142, no. 3 (June 2012): 525–61. http://dx.doi.org/10.1017/s0308210510001071.

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We relate the geometric Poisson brackets on the 2-Grassmannian in ℝ4 and on the (2, 2) Möbius sphere. We show that, when written in terms of local moving frames, the geometric Poisson bracket on the Möbius sphere does not restrict to the space of differential invariants of Schwarzian type. But when the concept of conformal natural frame is transported from the conformal sphere into the Grassmannian, and the Poisson bracket is written in terms of the Grassmannian natural frame, it restricts and results in either a decoupled system or a complexly coupled system of Korteweg–de Vries (KdV) equations, depending on the character of the invariants. We also show that the bi-Hamiltonian Grassmannian geometric brackets are equivalent to the non-commutative KdV bi-Hamiltonian structure. Both integrable systems and Hamiltonian structure can be brought back to the conformal sphere.
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Dissertations / Theses on the topic "Poisson brackets"

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Damianou, Pantelis Andrea. "Nonlinear Poisson brackets." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184704.

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A hierarchy of vector fields (master symmetries) and homogeneous nonlinear Poisson structures associated with the Toda lattice are constructed and the various connections between them are investigated. Among their properties: new brackets are generated from old ones by using Lie-derivatives in the direction of certain vector fields; the infinite sequences obtained consist of compatible Poisson brackets in which the constants of motion for the Toda lattice are in involution. The vector fields in the construction are unique up to addition of a Hamiltonian vector field. Similarly the Poisson brackets are unique up to addition of a trivial Poisson bracket. These are Poisson tensors generated by wedge products of Hamiltonian vector fields. The non-trivial brackets may also be obtained by the use of r-matrices; we give formulas and prove this for the quadratic and cubic Toda brackets. We also indicate how these results can be generalized to other (semisimple) Toda flows and we give explicit formulas for the rank 2 Lie algebra of type B₂. The main tool in this calculation is Dirac's constraint bracket formula. Finally we study nonlinear Poisson brackets associated with orbits through nilpotent conjugacy classes in gl(n, R) and formulate some conjectures. We determine the degree of the transverse Poisson structure through such nilpotent elements in gl(n, R) for n ≤ 7. This is accomplished also by the use of Dirac's bracket formula.
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Garcia-Naranjo, Luis Constantino. "Almost Poisson Brackets for Nonholonomic Systems on Lie Groups." Diss., The University of Arizona, 2007. http://hdl.handle.net/10150/195845.

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We present a geometric construction of almost Poisson brackets for nonholonomic mechanical systems whose configuration space is a Lie group G. We study the so-called LL and LR systems where the kinetic energy defines a left invariant metric on G and the constraints are invariant with respect to left (respectively right) translation on G.For LL systems, the equations on the momentum phase space, T*G, can be left translated onto g*, the dual space of the Lie algebra g. We show that the reduced equations on g* can be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the standard Lie-Poisson bracket onto the constraint space.For LR systems, we use ideas of semidirect product reduction to transfer the equations on T*G into the dual Lie algebra, s*, of a semidirect product. This provides a natural Lie algebraic setting for the equations of motion commonly found in the literature. We show that these equations can also be cast in Poisson form with respect to an almost Poisson bracket that is obtained by projecting the Lie-Poisson structure on s* onto a constraint submanifold.In both cases the constraint functions are Casimirs of the bracket and are satisfied automatically. Our construction is a natural generalization of the classical ideas of Lie-Poisson and semidirect product reduction to the nonholonomic case. It also sets a convenient stage for the study of Hamiltonization of certain nonholonomic systems.Our examples include the Suslov and the Veselova problems of constrained motion of a rigid body, and the Chaplygin sleigh.In addition we study the almost Poisson reduction of the Chaplygin sphere. We show that the bracket given byBorisov and Mamaev is obtained by reducing a nonstandard almost Poisson bracket that is obtained by projecting a non-canonical bivector onto the constraint submanifold using the Lagrange-D'Alembert principle.The examples that we treat show that it is possible to cast the reduced equations of motion of certain nonholonomic systems in Hamiltonian form (in the Poisson formulation) either by multiplication by a conformal factor, by the use of nonstandard brackets or simply by reduction methods.
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Thiffeault, Jean-Luc. "Classification, Casimir invariants, and stability of lie-poisson systems /." Digital version accessible at:, 1998. http://wwwlib.umi.com/cr/utexas/main.

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Kirchhoff-Lukat, Charlotte Sophie. "Aspects of generalized geometry : branes with boundary, blow-ups, brackets and bundles." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283007.

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This thesis explores aspects of generalized geometry, a geometric framework introduced by Hitchin and Gualtieri in the early 2000s. In the first part, we introduce a new class of submanifolds in stable generalized complex manifolds, so-called Lagrangian branes with boundary. We establish a correspondence between stable generalized complex geometry and log symplectic geometry, which allows us to prove results on local neighbourhoods and small deformations of this new type of submanifold. We further investigate Lefschetz thimbles in stable generalized complex Lefschetz fibrations and show that Lagrangian branes with boundary arise in this context. Stable generalized complex geometry provides the simplest examples of generalized complex manifolds which are neither complex nor symplectic, but it is sufficiently similar to symplectic geometry for a multitude of symplectic results to generalize. Our results on Lefschetz thimbles in stable generalized complex geometry indicate that Lagrangian branes with boundary are part of a potential generalisation of the Wrapped Fukaya category to stable generalized complex manifolds. The work presented in this thesis should be seen as a first step towards the extension of Floer theory techniques to stable generalized complex geometry, which we hope to develop in future work. The second part of this thesis studies Dorfman brackets, a generalisation of the Courant- Dorfman bracket, within the framework of double vector bundles. We prove that every Dorfman bracket can be viewed as a restriction of the Courant-Dorfman bracket on the standard VB-Courant algebroid, which is in this sense universal. Dorfman brackets have previously not been considered in this context, but the results presented here are reminiscent of similar results on Lie and Dull algebroids: All three structures seem to fit into a more general duality between subspaces of sections of the standard VB-Courant algebroid and brackets on vector bundles of the form T M ⊕ E ∗ , E → M a vector bundle. We establish a correspondence between certain properties of the brackets on one, and the subspaces on the other side.
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Yildirim, Selma. "Magnetic Spherical Pendulum." Master's thesis, METU, 2003. http://etd.lib.metu.edu.tr/upload/1086669/index.pdf.

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The magnetic spherical pendulum is a mechanical system consisting of a pendulum whereof the bob is electrically charged, moving under the influence of gravitation and the magnetic field induced by a magnetic monopole deposited at the origin. Physically not directly realizable, it turns out to be equivalent to a reduction of the Lagrange top. This work is essentially the logbook of our attempts at understanding the simplest contemporary approaches to the magnetic spherical pendulum.
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Lano, Ralph Peter. "Application of co-adjoint orbits to the loop group and the diffeomorphism group of the circle." Thesis, University of Iowa, 1994. https://ir.uiowa.edu/etd/5393.

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Vizarreta, Eber Daniel Chuño. "Sobre reticulados de Coxeter-Toda." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-28072016-142742/.

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Esse trabalho visa a investigar a estrutura bi-Hamiltoniana de uma classe de sistemas dinâmicos. Depois de introduzir as ferramentas necessárias, a saber, as noções de variedade de Poisson, de grupo de PoissonLieedenetworknodiscoenoanêl,introduziremosossistemasdinâmicos relevantes nessa dissertação, chamados de reticulados de Coxeter-Toda. Esses sistemas dinâmicos, cujo espaço de fase pode ser identicado com umoportunoquocientedeumacéluladupladeCoxeter-Bruhatdogrupo linear geral, são obtidos por redução do sistema de Toda em GLn. Na parte nal do presente trabalho apresentaremos alguns resultados relacionado à um sistema dinâmico discreto chamado de aplicação do pentagrama, o qual pode ser obtido através uma oportuna discretização do sistema dinâmico de Boussinesq.
This work aims to study the bi-Hamiltonian structure of a class of dynamical systems. After introducing the relevant tools, namely the notions of Poisson manifold, Poisson-Lie group and of network dened in a disc and in an annulus, we will introduce the dynamical systems of interest for this dissertation, i.e., the Coxeter-Toda lattices. These dynamical systems, whose phase-space can be identied with a suitable quotient of a Coxeter double Bruhat cell of the general linear group, are obtained by reduction starting from the Toda ow on GLn. In the nal part of the present work will be presented some results concerning a discrete integrable system close to the so called Pentagram map, which is a discretization of the Boussinesq dynamical system..
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Ogunbiyi, Adetokunbo Olawale. "Aspects of the toxicology of the bracken fern (Pteridium aquilinum)." Thesis, University of Surrey, 1987. http://epubs.surrey.ac.uk/844019/.

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Aspects of the toxicology of bracken (Pteridium aguilinum) were studied in sub-acute and chronic studies using male Wistar-albino rats. In a chronic study, bracken induced ileal adenomas in an 8.5 month period but after 24 months, no tumours were seen in both the quercetin- and shikimate-fed rats. Tissue ornithine decarboxylase (ODC) levels were enhanced over a 90-day test period when shikimate was fed alone or in conjunction with BBN and MNNG as initiators and with cyclophosphamide, saccharin and lithocholate as promoters, suggesting that shikimate might be a tumour promoter. Quercetin, was able to enhance ODC levels in conjunction with cyclophosphamide, BBN and MNNG as initiators and with cyclophosphamide, saccharin and lithocholate as promoters. However, it did not enhance tissue ODC levels when administered alone. Bracken, shikimate and quercetin induced a macrocytic, normochromic, non-regenerative anaemia with thrombocytopenia and granulocytopenia at the termination of the 90-day study. The bracken-induced ataxia of monogastrics was attributed additionally to nitrite and cyanide, due to the very high levels found in the urine and serum respectively of bracken-fed rats over a 28-day test period. The high urinary nitrite levels of the bracken-fed rats prompted an investigation into the role of N-nitrosation in bracken-induced carcinogenesis. To this end, the Nitrosation Assay period (NAP) revealed the presence of nitrosatable entities in the gut of the bracken-, quercetin- and shikimate-fed rats and in the urine of the bracken- and quercetin-fed rats. This suggests that nitrosation, probably via the formation of nitrosamides, might be an important mechanism for the mediation of bracken-induced carcinogenesis. The plausibility of explaining various aspects of the sub-acute and chronic toxicity of bracken in monogastrics and ruminants on the basis of a "nitrosamide hypothesis" is discussed.
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Ngomuo, Ahmed Juma. "Genotoxicity studies of the bracken fern constituents quercetin, shikimate and ptaquiloside in vitro in salmonella typhimurium and in vivo in rats and mice." Thesis, University of Surrey, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.317326.

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Pasqua, Michael. "Batalin-Vilkovisky quantization method with applications to gauge fixing." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/17071/.

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In una serie di articoli pubblicati tra il 1981 e il 1983, Igor Batalin e Grigory Vilkovisky svilupparono una procedura per quantizzare le teorie di gauge tramite un approccio basato sull’integrazione funzionale. Al giorno d’oggi questo è considerato il metodo più potente per la quantizzazione delle teorie di gauge. Lo scopo di questa tesi è l’applicazione del formalism BV ad alcune teorie di campo quantistiche topologiche di tipo Schwarz. E’ presentata una formulazione BV della celebre teoria di Chern-Simons, la quale fu la prima teoria di campo quantistica topologica ad essere studiata da Witten nel suo famoso articolo del 1989. Di seguito viene presentata la cosiddetta teoria di campo BF (probabilmente introdotta per la prima volta da Horowitz) su una varieta' di dimensione arbitraria in una prospettiva BV. L’ultima applicazione che consideriamo è la formulazione BV del modello Sigma di Poisson introdotto da Cattaneo e Felder. In tutti questi modelli viene discussa dettagliatamente la procedura di gauge fixing.
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Books on the topic "Poisson brackets"

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Voronov, Theodore, ed. Quantization, Poisson Brackets and Beyond. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/conm/315.

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Karasev, M. V. Nonlinear Poisson brackets: Geometry and quantization. Providence, R.I: American Mathematical Society, 1993.

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J, Grabowski, Urbański Paweł, and Zakrzewski Stanisław 1951-1998, eds. Poisson geometry: Stanisław Zakrzewski in memoriam. Warszawa: Institute of Mathematics, Polish Academy of Sciences, 2000.

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1963-, Voronov Theodore, ed. Quantization, Poisson brackets, and beyond: London Mathematical Society Regional Meeting and workshop on quantization, deformantions, and new homological and categorical methods in mathematical physics : July 6-13, 2001, University of Manchester Institute of Science and Technology, Manchester, United Kingdom. Providence, R.I: American Mathematical Society, 2002.

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Beris, Antony N. Thermodynamics of flowing systems: With internal microstructure. New York: Oxford University Press, 1994.

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Mann, Peter. Poisson Brackets & Angular Momentum. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0017.

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This chapter discusses canonical transformations and gauge transformations and is divided into three sections. In the first section, canonical coordinate transformations are introduced to the reader through generating functions as the extension of point transformations used in Lagrangian mechanics, with the harmonic oscillator being used as an example of a canonical transformation. In the second section, gauge theory is discussed in the canonical framework and compared to the Lagrangian case. Action-angle variables, direct conditions, symplectomorphisms, holomorphic variables, integrable systems and first integrals are examined. The third section looks at infinitesimal canonical transformations resulting from functions on phase space. Ostrogradsky equations in the canonical setting are also detailed.
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Baulieu, Laurent, John Iliopoulos, and Roland Sénéor. Quantum Field Theories with a Large Number of Fields. Oxford University Press, 2017. http://dx.doi.org/10.1093/oso/9780198788393.003.0023.

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The large N limit of field theories is studied for fields belonging to the vector representation of O(N) and the adjoint representation of SU(N). The first case gives a solvable model while in the second case a classical field theory may emerge with the commutators replaced by Poisson brackets.
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Lectures on Poisson Geometry. American Mathematical Society, 2021.

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Lectures on Poisson Geometry. American Mathematical Society, 2021.

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Mann, Peter. Linear Algebra. Oxford University Press, 2018. http://dx.doi.org/10.1093/oso/9780198822370.003.0037.

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This chapter is key to the understanding of classical mechanics as a geometrical theory. It builds upon earlier chapters on calculus and linear algebra and frames theoretical physics in a new and useful language. Although some degree of mathematical knowledge is required (from the previous chapters), the focus of this chapter is to explain exactly what is going on, rather than give a full working knowledge of the subject. Such an approach is rare in this field, yet is ever so welcome to newcomers who are exposed to this material for the first time! The chapter discusses topology, manifolds, forms, interior products, pullback and pushforward, as well as tangent bundles, cotangent bundles, jet bundles and principle bundles. It also discusses vector fields, integral curves, flow, exterior derivatives and fibre derivatives. In addition, Lie derivatives, Lie brackets, Lie algebra, Lie–Poisson brackets, vertical space, horizontal space, groups and algebroids are explained.
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Book chapters on the topic "Poisson brackets"

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Cardin, Franco. "Poisson Brackets Environment." In Lecture Notes of the Unione Matematica Italiana, 67–72. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-11026-4_3.

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Strocchi, Franco. "Poisson brackets and canonical structure." In A Primer of Analytical Mechanics, 43–55. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-73761-4_4.

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Unterberger, André. "Quantization, products and Poisson brackets." In Lecture Notes in Mathematics, 177–90. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/bfb0104053.

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Vorob'ev, Yu M., and M. V. Karasev. "Deformation and cohomologies of Poisson brackets." In Lecture Notes in Mathematics, 271–89. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/bfb0085961.

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Kosmann-Schwarzbach, Y. "Graded Poisson Brackets and Field Theory." In Modern Group Theoretical Methods in Physics, 189–96. Dordrecht: Springer Netherlands, 1995. http://dx.doi.org/10.1007/978-94-015-8543-9_17.

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Oevel, W. "Poisson Brackets for Integrable Lattice Systems." In Algebraic Aspects of Integrable Systems, 261–83. Boston, MA: Birkhäuser Boston, 1997. http://dx.doi.org/10.1007/978-1-4612-2434-1_13.

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Roubtsov, V., and T. Skrypnyk. "Compatible Poisson brackets, quadratic Poisson algebras and classical r-matrices." In Differential Equations - Geometry, Symmetries and Integrability, 311–33. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-00873-3_15.

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Korovnichenko, A., and A. Zhedanov. "Dual Algebras with Non-Linear Poisson Brackets." In Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory, 265–72. Dordrecht: Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-010-0670-5_16.

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Sharapov, A. A. "On Covariant Poisson Brackets in Field Theory." In Trends in Mathematics, 177–86. Cham: Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-18212-4_12.

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Sokolov, Vladimir. "Elliptic Calogero-Moser Hamiltonians and Compatible Poisson Brackets." In Recent Developments in Integrable Systems and Related Topics of Mathematical Physics, 38–46. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-04807-5_4.

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Conference papers on the topic "Poisson brackets"

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Kennedy, Anthony D., Michael A. Clark, and Paulo Silva. "Tuning HMC using Poisson Brackets." In The XXVI International Symposium on Lattice Field Theory. Trieste, Italy: Sissa Medialab, 2009. http://dx.doi.org/10.22323/1.066.0041.

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Khudaverdian, H. M., Th Th Voronov, Piotr Kielanowski, Anatol Odzijewicz, Martin Schlichenmaier, and Theodore Voronov. "Higher Poisson Brackets and Differential Forms." In GEOMETRIC METHODS IN PHYSICS. AIP, 2008. http://dx.doi.org/10.1063/1.3043861.

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MIGNEMI, S. "NONCANONICAL POISSON BRACKETS IN DEFORMED SPECIAL RELATIVITY." In Proceedings of the 12th Conference on WASCOM 2003. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702937_0037.

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Minano, Juan C. "Poisson brackets method of design of nonimaging concentrators: a review." In SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, edited by Roland Winston and Robert L. Holman. SPIE, 1993. http://dx.doi.org/10.1117/12.161936.

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Maschke, B. M. J., and A. J. van der Schaft. "Hamiltonian Systems, Pseudo-Poisson Brackets and Their Scattering Representation for Physical Systems." In ASME 1999 Design Engineering Technical Conferences. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/detc99/vib-8007.

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Abstract This paper is concerned with the definition of the geometric structure of Hamiltonian systems associated with energy–conserving systems in relation with an interconnection topology of their network model. It is also presented how the symplectic structure of standard Hamiltonian systems has to be extended to pseudo–Poisson tensors in order to cope with invariants, equilibria and constraints. Finally a scattering representation of these pseudo–Poisson tensors is defined.
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FLORES–ESPINOZA, RUBEN, and YU M. VOROBJEV. "RELATIVISTIC CORRECTIONS TO ELEMENTARY GALILEAN DYNAMICS AND DEFORMATIONS OF POISSON BRACKETS." In Proceedings of the III International Symposium. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792099_0009.

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SOROKA, D. V., and V. A. SOROKA. "EXTERIOR DIFFERENTIALS IN SUPERSPACE AND POISSON BRACKETS OF DIVERSE GRASSMANN PARITIES." In Proceedings of the IX International Conference. WORLD SCIENTIFIC, 2002. http://dx.doi.org/10.1142/9789812778192_0074.

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8

Jean-Louis, K. M., R. M. Lollchund, and F. X. Giraldo. "Computational Analysis of Potential Vorticity and Quasi-Geostrophic Approximation for the Quasi-Hydrostatics Thermal Rotating Shallow Water Equations." In Topical Problems of Fluid Mechanics 2023. Institute of Thermomechanics of the Czech Academy of Sciences; CTU in Prague Faculty of Mech. Engineering Dept. Tech. Mathematics, 2023. http://dx.doi.org/10.14311/tpfm.2023.011.

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Abstract:
A novel idealized and incompressible fluid flow governing model is introduced, namely, the two-dimensional quasi-hydrostatics thermal rotating shallow water equations. The potential vorticity for the new model is computationally analyzed through the Hamiltonian formulation of the Eulerian variables using the noncanonical Poisson brackets. Both similarities and differences are observed between the new and standard shallow models.
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MOKHOV, O. I. "COMPATIBLE NONLOCAL POISSON BRACKETS OF HYDRODYNAMIC TYPE AND INTEGRABLE REDUCTIONS OF THE LAMÉ EQUATIONS." In Proceedings of the Workshop. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704467_0028.

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Oevel, Walter, and Klaus Strack. "The Yang-Baxter equation and a systematic search for Poisson brackets on associative algebras." In the 1991 international symposium. New York, New York, USA: ACM Press, 1991. http://dx.doi.org/10.1145/120694.120728.

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Reports on the topic "Poisson brackets"

1

Mokhov, Oleg I. Multidimentional Poisson Brackets of Hydrodynamic Type and Flat Pencils of Metrics. Journal of Geometry and Symmetry in Physics, 2012. http://dx.doi.org/10.7546/jgsp-10-2007-51-72.

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2

Brizard, A. Gyrokinetic energy conservation and Poisson-bracket formulation. Office of Scientific and Technical Information (OSTI), November 1988. http://dx.doi.org/10.2172/6866694.

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