References of "Communications in Mathematical Physics"
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See detailNodal Statistics of Planar Random Waves
Nourdin, Ivan UL; Peccati, Giovanni UL; Rossi, Maurizia

in Communications in Mathematical Physics (2019), 369(1), 99-151

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See detailAn explicit two step quantization of Poisson structures and Lie bialgebras
Merkulov, Sergei UL; Willwacher, Thomas

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 ▲]

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See detailFormal connections for families of star products
Andersen, Joergen; Masulli, Paolo; Schatz, Florian UL

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 ▲]

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See detailConformally equivariant quantization for spinning particles
Michel, Jean-Philippe UL

in Communications in Mathematical Physics (2015), 333(1), 261298

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See detail5D super Yang-Mills on Yp,q Sasaki-Einstein manifolds
Qiu, Jian UL; Zabzine, Maxim

in Communications in Mathematical Physics (2015), 333(2),

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See detailRozansky-Witten-type invariants from symplectic Lie pairs
Voglaire, Yannick UL; Xu, Ping

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 ▲]

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See detailQuantization of Poisson manifolds from the integrability of the modular function
Bonechi, Francesco; Tarlini, Marco; Ciccoli, Nicola 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 ▲]

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See detailCollisions of particles in locally AdS spacetimes II. Moduli of globally hyperbolic spaces
Barbot, Thierry; Bonsante, Francesco; Schlenker, Jean-Marc UL

in Communications in Mathematical Physics (2014), 327(3), 691-735

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See detailFourth moment theorem and q-Brownian chaos
Deya, Aurélien; Noreddine, Salim; Nourdin, Ivan UL

in Communications in Mathematical Physics (2013), 321(1), 113-134

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See detailDifferential and Twistor Geometry of the Quantum Hopf Fibration
Brain, Simon UL; Landi, Giovanni

in Communications in Mathematical Physics (2012), 315(2), 489-530

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See detailFeynman integrals and motives of configuration spaces
Ceyhan, Ozgur UL; Marcolli, Matilde

in Communications in Mathematical Physics (2012), 313

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See detailCollisions of particles in locally AdS spacetimes I. Local description and global examples
Barbot, Thierry; Bonsante, Francesco; Schlenker, Jean-Marc UL

in Communications in Mathematical Physics (2011), 308(1), 147--200

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See detailWheeled Pro(p)file of Batalin-Vilkovisky formalism
Merkulov, Sergei UL

in Communications in Mathematical Physics (2010), 295(3), 585638

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See detailBFV-complex and higher homotopy structures
Schatz, Florian UL

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 ▲]

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See detailOn the renormalized volume of hyperbolic 3-manifolds
Krasnov, Kirill; Schlenker, Jean-Marc UL

in Communications in Mathematical Physics (2008), 279(3), 637--668

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See detailGlobal Geometric Deformations of the Virasoro algebra, current and affine algebras by Krichever-Novikov type algebras
Fialowski, Alice; Schlichenmaier, Martin UL

in Communications in Mathematical Physics (2007), 46(11), 2708-2724

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See detailGlobal geometric deformations of current algebras as Krichever-Novikov type algebras
Fialowski, Alice; Schlichenmaier, Martin UL

in Communications in Mathematical Physics (2005), 260(3), 579-612

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See detailToeplitz quantization of Kähler manifolds and gl(N), N to infinity, limits
Bordemann, Martin UL; Meinrenken, Eckhard; Schlichenmaier, Martin UL

in Communications in Mathematical Physics (1994), 165

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See detailgl(∞) and geometric quantization
Bordemann, Martin UL; Hoppe, Jens; Schaller, Peter et al

in Communications in Mathematical Physics (1991), 138(2), 209-244

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