GROUPOIDS, LOOP SPACES AND QUANTIZATION OF 2-PLECTIC MANIFOLDS

DOI10.1142/S0129055X13300057zbMath1276.81085arXiv1211.0395OpenAlexW3102061911MaRDI QIDQ5299774

Christian Sämann, Richard J. Szabo

Publication date: 21 June 2013

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0395

zbMATH Keywords

quantizationmultisymplectic geometryloop spacesgroupoids

Mathematics Subject Classification ID

Quantization in field theory; cohomological methods (81T70) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30) Loop spaces (55P35) Geometry and quantization, symplectic methods (81S10) Geometric quantization (53D50) Groupoids, semigroupoids, semigroups, groups (viewed as categories) (18B40)

Related Items (16)

Lie 2-algebra models ⋮ Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry ⋮ (Non-)commutative closed string on T-dual toroidal backgrounds ⋮ Higher affine connections ⋮ Non-geometric fluxes, quasi-Hopf twist deformations, and nonassociative quantum mechanics ⋮ Fluxes, bundle gerbes and 2-Hilbert spaces ⋮ Double field theory and membrane sigma-models ⋮ Quantization of Magnetic Poisson Structures ⋮ Quantum field theoretic representation of Wilson surfaces. I: Higher coadjoint orbit theory ⋮ The 2-Hilbert space of a prequantum bundle gerbe ⋮ BEREZIN–TOEPLITZ QUANTIZATION, HYPERKÄHLER MANIFOLDS, AND MULTISYMPLECTIC MANIFOLDS ⋮ On the gauge features of gravity on a Lie algebroid structure ⋮ Double field theory and geometric quantisation ⋮ On the prequantisation map for 2-plectic manifolds ⋮ Brane current algebras and generalised geometry from QP manifolds. Or, ``when they go high, we go low ⋮ Field equations and radial solutions in a noncommutative spherically symmetric geometry

Cites Work

• Leibniz algebroids, twistings and exceptional generalized geometry
• The quantization of the symplectic groupoid of the standard Podlès sphere
• Holonomy on \(D\)-branes
• Constructing self-dual strings
• Nonassociative tori and applications to \(T\)-duality
• A groupoid approach to quantization
• Categorified symplectic geometry and the classical string
• The \(sh\) Lie structure of Poisson brackets in field theory
• Loop spaces as complex manifolds
• On foundation of the generalized Nambu mechanics
• Toeplitz quantization of Kähler manifolds and \(gl(N)\), \(N\to \infty\) limits
• Manin triples for Lie bialgebroids
• Integrability of Lie brackets
• The moduli space of complex Lagrangian submanifolds
• Transgression to loop spaces and its inverse. III: Gerbes and thin fusion bundles
• Integrability of Poisson brackets
• Twisted \(K\)-theory and \(K\)-theory of bundle gerbes
• Integration of twisted Dirac brackets
• Some remarks concerning Nambu mechanics
• Integrability of Jacobi and Poisson structures
• Prequantization and Lie brackets
• Nonassociative gravity in string theory?
• Non-geometric fluxes, asymmetric strings and nonassociative geometry
• Bundle Gerbes: Stable Isomorphism and Local Theory
• Lie Group Convolution Algebras as Deformation Quantizations of Linear Poisson Structures
• κ -Minkowski representations on Hilbert spaces
• n-ary algebras: a review with applications
• COHERENT STATES AND KAHLER MANIFOLDS
• Generalized Hamiltonian Dynamics
• Symplectic groupoids and Poisson manifolds
• Quantized Nambu–Poisson manifolds and n-Lie algebras
• Bundle Gerbes
• THE POISSON BRACKET FOR POISSON FORMS IN MULTISYMPLECTIC FIELD THEORY
• Constructing smooth manifolds of loop spaces
• D-branes in a topologically nontrivial \(B\)-field
• A noncommutative M-theory five-brane
• Higher-dimensional parallel transports

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