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Nodal Statistics of Planar Random Waves Nourdin, Ivan ; Peccati, Giovanni ; in Communications in Mathematical Physics (in press) Detailed reference viewed: 74 (8 UL)An explicit two step quantization of Poisson structures and Lie bialgebras Merkulov, Sergei ; in Communications in Mathematical Physics (2018), 364(2), 505578 We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a ... [more ▼] We develop a new approach to deformation quantizations of Lie bialgebras and Poisson structures which goes in two steps. In the first step one associates to any Poisson (resp. Lie bialgebra) structure a so called quantizable Poisson (resp. Lie bialgebra) structure. We show explicit transcendental formulae for this correspondence. In the second step one deformation quantizes a quantizable Poisson (resp. Lie bialgebra) structure. We show again explicit transcendental formulae for this second step correspondence (as a byproduct we obtain configuration space models for biassociahedron and bipermutohedron). In the Poisson case the first step is the most non-trivial one and requires a choice of an associator while the second step quantization is essentially unique, it is independent of a choice of an associator and can be done by a trivial induction. We conjecture that similar statements hold true in the case of Lie bialgebras. The main new result is a surprisingly simple explicit universal formula (which uses only smooth differential forms) for universal quantizations of finite-dimensional Lie bialgebras. [less ▲] Detailed reference viewed: 94 (5 UL)Formal connections for families of star products ; ; Schatz, Florian in Communications in Mathematical Physics (2016), 342(2), 739-768 We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points ... [more ▼] We define the notion of a formal connection for a smooth family of star products with fixed underlying symplectic structure. Such a formal connection allows one to relate star products at different points in the family. This generalizes the formal Hitchin connection defined in. We establish a necessary and sufficient condition that guarantees the existence of a formal connection, and we describe the space of formal connections for a family as an affine space modelled by the derivations of the star products. Moreover we show that if the parameter space has trivial first cohomology group any two flat formal connections are related by an automorphism of the family of star products. [less ▲] Detailed reference viewed: 45 (4 UL)Conformally equivariant quantization for spinning particles Michel, Jean-Philippe in Communications in Mathematical Physics (2015), 333(1), 261298 Detailed reference viewed: 17 (0 UL)5D super Yang-Mills on Yp,q Sasaki-Einstein manifolds Qiu, Jian ; in Communications in Mathematical Physics (2015), 333(2), Detailed reference viewed: 17 (1 UL)Rozansky-Witten-type invariants from symplectic Lie pairs Voglaire, Yannick ; in Communications in Mathematical Physics (2014) We introduce symplectic structures on “Lie pairs” of (real or complex) Lie algebroids as studied by Chen et al. (From Atiyah classes to homotopy Leibniz algebras. arXiv:1204.1075, 2012), encompassing ... [more ▼] We introduce symplectic structures on “Lie pairs” of (real or complex) Lie algebroids as studied by Chen et al. (From Atiyah classes to homotopy Leibniz algebras. arXiv:1204.1075, 2012), encompassing homogeneous symplectic spaces, symplectic manifolds with a g-action, and holomorphic symplectic manifolds. We show that to each such symplectic Lie pair are associated Rozansky–Witten-type invariants of three-manifolds and knots, given respectively by weight systems on trivalent and chord diagrams. [less ▲] Detailed reference viewed: 87 (10 UL)Quantization of Poisson manifolds from the integrability of the modular function ; ; et al in Communications in Mathematical Physics (2014), 331(2), 851885 We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid ... [more ▼] We discuss a framework for quantizing a Poisson manifold via the quantization of its symplectic groupoid, that combines the tools of geometric quantization with the results of Renault's theory of groupoid C*-algebras. This setting allows very singular polarizations. In particular we consider the case when the modular function is "multiplicatively integrable", i.e. when the space of leaves of the polarization inherits a groupoid structure. If suitable regularity conditions are satisfied, then one can define the quantum algebra as the convolution algebra of the subgroupoid of leaves satisfying the Bohr-Sommerfeld conditions. We apply this procedure to the case of a family of Poisson structures on CP_n, seen as Poisson homogeneous spaces of the standard Poisson-Lie group SU(n+1). We show that a bihamiltoniam system on CP_n defines a multiplicative integrable model on the symplectic groupoid; we compute the Bohr-Sommerfeld groupoid and show that it satisfies the needed properties for applying Renault theory. We recover and extend Sheu's description of quantum homogeneous spaces as groupoid C*-algebras. [less ▲] Detailed reference viewed: 87 (7 UL)Collisions of particles in locally AdS spacetimes II. Moduli of globally hyperbolic spaces ; ; Schlenker, Jean-Marc in Communications in Mathematical Physics (2014), 327(3), 691-735 Detailed reference viewed: 46 (5 UL)Fourth moment theorem and q-Brownian chaos ; ; Nourdin, Ivan in Communications in Mathematical Physics (2013), 321(1), 113-134 Detailed reference viewed: 50 (1 UL)Differential and Twistor Geometry of the Quantum Hopf Fibration Brain, Simon ; in Communications in Mathematical Physics (2012), 315(2), 489-530 Detailed reference viewed: 28 (0 UL)Feynman integrals and motives of configuration spaces Ceyhan, Ozgur ; in Communications in Mathematical Physics (2012), 313 Detailed reference viewed: 84 (2 UL)Collisions of particles in locally AdS spacetimes I. Local description and global examples ; ; Schlenker, Jean-Marc in Communications in Mathematical Physics (2011), 308(1), 147--200 Detailed reference viewed: 30 (1 UL)Wheeled Pro(p)file of Batalin-Vilkovisky formalism Merkulov, Sergei in Communications in Mathematical Physics (2010), 295(3), 585638 Detailed reference viewed: 44 (2 UL)BFV-complex and higher homotopy structures Schatz, Florian in Communications in Mathematical Physics (2009), 286(2), 399443 We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold ... [more ▼] We present a connection between the BFV-complex (abbreviation for Batalin-Fradkin-Vilkovisky complex) and the strong homotopy Lie algebroid associated to a coisotropic submanifold of a Poisson manifold. We prove that the latter structure can be derived from the BFV-complex by means of homotopy transfer along contractions. Consequently the BFV-complex and the strong homotopy Lie algebroid structure are L-infinity quasi-isomorphic and control the same formal deformation problem. However there is a gap between the non-formal information encoded in the BFV-complex and in the strong homotopy Lie algebroid respectively. We prove that there is a one-to-one correspondence between coisotropic submanifolds given by graphs of sections and equivalence classes of normalized Maurer-Cartan elemens of the BFV-complex. This does not hold if one uses the strong homotopy Lie algebroid instead. [less ▲] Detailed reference viewed: 48 (0 UL)On the renormalized volume of hyperbolic 3-manifolds ; Schlenker, Jean-Marc in Communications in Mathematical Physics (2008), 279(3), 637--668 Detailed reference viewed: 48 (2 UL)Global Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras ; Schlichenmaier, Martin in Communications in Mathematical Physics (2007), 46(11), 2708-2724 Detailed reference viewed: 25 (0 UL)Global geometric deformations of current algebras as Krichever-Novikov type algebras ; Schlichenmaier, Martin in Communications in Mathematical Physics (2005), 260(3), 579-612 Detailed reference viewed: 28 (0 UL)Toeplitz quantization of Kähler manifolds and gl(N), N to infinity, limits Bordemann, Martin ; ; Schlichenmaier, Martin in Communications in Mathematical Physics (1994), 165 Detailed reference viewed: 21 (2 UL)gl(∞) and geometric quantization Bordemann, Martin ; ; et al in Communications in Mathematical Physics (1991), 138(2), 209-244 Detailed reference viewed: 81 (13 UL) |
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