Relevant bibliographies by topics / Hilbert manifold structure

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Hilbert manifold structure'

Author: Grafiati
Published: 4 June 2021
Last updated: 8 February 2022

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Journal articles on the topic "Hilbert manifold structure"

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ANIELLO, P., G. MARMO, and G. F. VOLKERT. "CLASSICAL TENSORS FROM QUANTUM STATES." International Journal of Geometric Methods in Modern Physics 06, no. 03 (2009): 369–83. http://dx.doi.org/10.1142/s0219887809003576.

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The embedding of a manifold M into a Hilbert-space ℍ induces, via the pull-back, a tensor field on M out of the Hermitian tensor on ℍ. We propose a general procedure to compute these tensors in particular for Manifolds admitting a Lie-Group structure.
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PATÁK, A., and D. KRUPKA. "GEOMETRIC STRUCTURE OF THE HILBERT–YANG–MILLS FUNCTIONAL." International Journal of Geometric Methods in Modern Physics 05, no. 03 (2008): 387–405. http://dx.doi.org/10.1142/s0219887808002850.

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The global variational functional, defined by the Hilbert–Yang–Mills Lagrangian over a smooth manifold, is investigated within the framework of prolongation theory of principal fiber bundles, and global variational theory on fibered manifolds. The principal Lepage equivalent of this Lagrangian is constructed, and the corresponding infinitesimal first variation formula is obtained. It is shown, in particular, that the Noether currents, associated with isomorphisms of the underlying geometric structures, split naturally into several terms, one of which is the exterior derivative of the Komar–Yan
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Parsian, A., and A. Shafei Deh Abad. "Dirac structures on Hilbert spaces." International Journal of Mathematics and Mathematical Sciences 22, no. 1 (1999): 97–108. http://dx.doi.org/10.1155/s0161171299220972.

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For a real Hilbert space(H,〈,〉), a subspaceL⊂H⊕His said to be a Dirac structure onHif it is maximally isotropic with respect to the pairing〈(x,y),(x′,y′)〉+=(1/2)(〈x,y′〉+〈x′,y〉). By investigating some basic properties of these structures, it is shown that Dirac structures onHare in one-to-one correspondence with isometries onH, and, any two Dirac structures are isometric. It is, also, proved that any Dirac structure on a smooth manifold in the sense of [1] yields a Dirac structure on some Hilbert space. The graph of any densely defined skew symmetric linear operator on a Hilbert space is, also,
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ASANO, MASAKO. "ON A CLASS OF TOPOLOGICAL QUANTUM FIELD THEORIES IN THREE DIMENSIONS." International Journal of Modern Physics A 11, no. 25 (1996): 4577–96. http://dx.doi.org/10.1142/s0217751x96002121.

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We investigate the Chung–Fukuma–Shapere theory, or Kuperberg theory, of three-dimensional lattice topological field theory. We construct a functor which satisfies Atiyah’s axioms of topological quantum field theory by reformulating the theory as a Turaev–Viro type state sum theory on a triangulated manifold. This corresponds to giving the Hilbert space structure to the original theory. The theory can be extended to give a topological invariant of manifolds with boundary.
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Delay, Erwann, and Jérémie Fougeirol. "Hilbert manifold structure for weakly asymptotically hyperbolic relativistic initial data." Pure and Applied Mathematics Quarterly 17, no. 1 (2021): 443–501. http://dx.doi.org/10.4310/pamq.2021.v17.n1.a12.

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Radnell, David, Eric Schippers, and Wolfgang Staubach. "A Hilbert manifold structure on the Weil–Petersson class Teichmüller space of bordered Riemann surfaces." Communications in Contemporary Mathematics 17, no. 04 (2015): 1550016. http://dx.doi.org/10.1142/s0219199715500169.

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We consider bordered Riemann surfaces which are biholomorphic to compact Riemann surfaces of genus g with n regions biholomorphic to the disk removed. We define a refined Teichmüller space of such Riemann surfaces (which we refer to as the WP-class Teichmüller space) and demonstrate that in the case that 2g + 2 - n > 0, this refined Teichmüller space is a Hilbert manifold. The inclusion map from the refined Teichmüller space into the usual Teichmüller space (which is a Banach manifold) is holomorphic. We also show that the rigged moduli space of Riemann surfaces with non-overlapping holomor
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ISIDRO, JOSÉ M. "MODULI OF QUANTA." International Journal of Geometric Methods in Modern Physics 03, no. 02 (2006): 177–86. http://dx.doi.org/10.1142/s0219887806001089.

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The classical phase of the matrix model of 11-dimensional M-theory is complex, infinite-dimensional Hilbert space. As a complex manifold, the latter admits a continuum of nonequivalent, complex-differentiable structures that can be placed in 1-to-1 correspondence with families of coherent states in the Hilbert space of quantum states. The moduli space of nonbiholomorphic complex structures on classical phase space turns out to be an infinite-dimensional symmetric space. We argue that each choice of a complex differentiable structure gives rise to a physically different notion of an elementary
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Suri, Ali. "Isomorphism classes for higher order tangent bundles." Advances in Geometry 17, no. 2 (2017): 175–89. http://dx.doi.org/10.1515/advgeom-2017-0001.

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AbstractThe tangent bundle TkM of order k of a smooth Banach manifold M consists of all equivalence classes of curves that agree up to their accelerations of order k. In previous work the author proved that TkM, 1 ≤ k ≤∞, admits a vector bundle structure on M if and only if M is endowed with a linear connection, or equivalently if a connection map on TkM is defined. This bundle structure depends heavily on the choice of the connection. In this paper we ask about the extent to which this vector bundle structure remains isomorphic. To this end we define the k-th order differential Tkg : TkM ⟶ Tk
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CHIBA, HAYATO. "A proof of the Kuramoto conjecture for a bifurcation structure of the infinite-dimensional Kuramoto model." Ergodic Theory and Dynamical Systems 35, no. 3 (2013): 762–834. http://dx.doi.org/10.1017/etds.2013.68.

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AbstractThe Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as coupled phase oscillators. In this paper, a bifurcation structure of the infinite-dimensional Kuramoto model is investigated. A purpose here is to prove the bifurcation diagram of the model conjectured by Kuramoto in 1984; if the coupling strength $K$ between oscillators, which is a parameter of the system, is smaller than some threshold ${K}_{c} $, the de-synchronous state (trivial steady state) is asymptotically stable, while if $K$ exceeds ${K}_{c} $, a non-trivial s
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Naderi, F., A. Rezaei-Aghdam, and F. Darabi. "Gravity and induced matter on nearly Kähler manifolds." International Journal of Modern Physics A 30, no. 03 (2015): 1550015. http://dx.doi.org/10.1142/s0217751x15500153.

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We show that the conservation of energy–momentum tensor of a gravitational model with Einstein–Hilbert like action on a nearly Kähler manifold with the scalar curvature of a curvature-like tensor, is consistent with the nearly Kähler properties. In this way, the nearly Kähler structure is automatically manifested in the action as a induced matter field. As an example of nearly Kähler manifold, we consider the group manifold of R×II ×S3×S3 on which we identify a nearly Kähler structure and solve the Einstein equations to interpret the model. It is shown that the nearly Kähler structure in this
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Dissertations / Theses on the topic "Hilbert manifold structure"

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Fougeirol, Jérémie. "Structure de variété de Hilbert et masse sur l'ensemble des données initiales relativistes faiblement asymptotiquement hyperboliques." Thesis, Avignon, 2017. http://www.theses.fr/2017AVIG0417/document.

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La relativité générale est une théorie physique de la gravitation élaborée il y a un siècle, dans laquelle l'univers est modélisé par une variété Lorentzienne (N,gamma) de dimension 4 appelée espace-temps et vérifiant les équations d'Einstein. Lorsque l'on sépare la dimension temporelle des trois dimensions spatiales, les équations de contrainte découlent naturellement de la décomposition 3+1 des équations d'Einstein. Elles constituent une condition nécessaire et suffisante pour pouvoir considérer l'espace-temps N comme l'évolution temporelle d'une hypersurface Riemannienne (m,g) plongée dans
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Book chapters on the topic "Hilbert manifold structure"

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Pelletier, F. "Conic Sub-Hilbert–Finsler Structure on a Banach Manifold." In Trends in Mathematics. Springer International Publishing, 2019. http://dx.doi.org/10.1007/978-3-030-01156-7_26.

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