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Displaying 21 – 40 of 98

Quantification pour les paires symétriques et diagrammes de Kontsevich

Alberto S. Cattaneo, Charles Torossian (2008)

Annales scientifiques de l'École Normale Supérieure

In this article we use the expansion for biquantization described in [7] for the case of symmetric spaces. We introduce a function of two variables $E (X, Y)$ for any symmetric pairs. This function has an expansion in terms of Kontsevich’s diagrams. We recover most of the known results though in a more systematic way by using some elementary properties of this $E$ function. We prove that Cattaneo and Felder’s star product coincides with Rouvière’s for any symmetric pairs. We generalize some of Lichnerowicz’s...

Quantitative Bloch's theorem for certain classes of holomorphic mappings of the ball into Pn (C).

Kyong T. Hahn (1976)

Journal für die reine und angewandte Mathematik

Quantization and global properties of manifolds

G. I. Kolerov (1978)

Annales de l'I.H.P. Physique théorique

Quantization commutes with reduction in the non-compact setting: the case of holomorphic discrete series

Paul-Emile Paradan (2015)

Journal of the European Mathematical Society

In this paper we show that the multiplicities of holomorphic discrete series representations relative to reductive subgroups satisfy the credo “quantization commutes with reduction”.

Quantization of a dimensionally reduced Seiberg-Witten moduli space.

Dey, Rukmini (2004)

Mathematical Physics Electronic Journal [electronic only]

Quantization of pencils with a gl-type Poisson center and braided geometry

Dimitri Gurevich, Pavel Saponov (2011)

Banach Center Publications

We consider Poisson pencils, each generated by a linear Poisson-Lie bracket and a quadratic Poisson bracket corresponding to a so-called Reflection Equation Algebra. We show that any bracket from such a Poisson pencil (and consequently, the whole pencil) can be restricted to any generic leaf of the Poisson-Lie bracket. We realize a quantization of these Poisson pencils (restricted or not) in the framework of braided affine geometry. Also, we introduce super-analogs of all these Poisson pencils and...

Quantization of Poisson Hamiltonian systems

Chiara Esposito (2015)

Banach Center Publications

In this paper we recall the concept of Hamiltonian system in the canonical and Poisson settings. We will discuss the quantization of the Hamiltonian systems in the Poisson context, using formal deformation quantization and quantum group theories.

Quantization of Poisson structures on $𝐑^{2}$ .

Tamarkin, Dmitry (1997)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Quantization of the cotangent bundle via the tangent groupoid

José Cariñena, Jesús Clemente-Gallardo (2000)

Banach Center Publications

Quantization on submanifolds

Doebner, H. D., Tolar, J. (1984)

Proceedings of the 11th Winter School on Abstract Analysis

Quantized charge in terms of pure geometry

C. von Westenholz (1971)

Annales de l'I.H.P. Physique théorique

Quantum 4-sphere: the infinitesimal approach

F. Bonechi, M. Tarlini, N. Ciccoli (2003)

Banach Center Publications

We describe how the constructions of quantum homogeneous spaces using infinitesimal invariance and quantum coisotropic subgroups are related. As an example we recover the quantum 4-sphere of [2] through infinitesimal invariance with respect to $_{q} (S U (2))$ .

Quantum Cohomology and Crepant Resolutions: A Conjecture

Tom Coates, Yongbin Ruan (2013)

Annales de l’institut Fourier

We give an expository account of a conjecture, developed by Coates–Iritani–Tseng and Ruan, which relates the quantum cohomology of a Gorenstein orbifold $𝒳$ to the quantum cohomology of a crepant resolution $Y$ of $𝒳$ . We explore some consequences of this conjecture, showing that it implies versions of both the Cohomological Crepant Resolution Conjecture and of the Crepant Resolution Conjectures of Ruan and Bryan–Graber. We also give a ‘quantized’ version of the conjecture, which determines higher-genus...

Quantum cohomology and its application.

Ruan, Yongbin (1998)

Documenta Mathematica

Quantum Cohomology and Periods

Hiroshi Iritani (2011)

Annales de l’institut Fourier

In a previous paper, the author introduced an integral structure in quantum cohomology defined by the $K$ -theory and the Gamma class and showed that it is compatible with mirror symmetry for toric orbifolds. Applying the quantum Lefschetz principle to the previous results, we find an explicit relationship between solutions to the quantum differential equation of toric complete intersections and the periods (or oscillatory integrals) of their mirrors. We describe in detail the mirror isomorphism of...

Quantum cohomology of flag manifolds $G / B$ and quantum Toda lattices.

Kim, Bumsig (1999)

Annals of Mathematics. Second Series

Quantum deformation of relativistic supersymmetry

Sobczyk, Jan (1996)

Proceedings of the 15th Winter School "Geometry and Physics"

From the text: The author reviews recent research on quantum deformations of the Poincaré supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosiński, J. Lukierski, P. Maślanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct. As far...

Quantum deformations of the Lorentz group. The Hopf-algebra level

S. L. Woronowicz, S. Zakrzewski (1994)

Compositio Mathematica

Quantum Equivalent Magnetic Fields that Are Not Classically Equivalent

Carolyn Gordon, William Kirwin, Dorothee Schueth, David Webb (2010)

Annales de l’institut Fourier

We construct pairs of compact Kähler-Einstein manifolds $(M_{i}, g_{i}, ω_{i}) (i = 1, 2)$ of complex dimension $n$ with the following properties: The canonical line bundle $L_{i} = ⋀^{n} T^{*} M_{i}$ has Chern class $[ω_{i} / 2 π]$ , and for each positive integer $k$ the tensor powers $L_{1}^{\otimes k}$ and $L_{2}^{\otimes k}$ are isospectral for the bundle Laplacian associated with the canonical connection, while $M_{1}$ and $M_{2}$ – and hence $T^{*} M_{1}$ and $T^{*} M_{2}$ – are not homeomorphic. In the context of geometric quantization, we interpret these examples as magnetic fields which are quantum equivalent but not classically equivalent....

Quantum ergodicity of C*-dynamical systems

Steven Zelditch (1994/1995)

Séminaire de théorie spectrale et géométrie

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