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Star Products and Deformation Quantization

2017
Among the “flavors” of deformation quantization, there are two whose interplay informs much of Boutet de Monvel’s work on this subject. In the first, sometimes known as semiclassical, a commutative algebra to be deformed, with associativity retained, is augmented by an external parameter (Planck’s constant in the application to classical/quantum ...
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Some examples and applications of Fedosov's star products and deformation quantization

Czechoslovak Journal of Physics, 1998
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Cariñena, José F.   +1 more
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10. Perturbative Darboux Transformation and Deformation Quantization of the Kink-Antikink System - Explicit diagonalisation and the star product for interacting solitons

Starting from the exact canonical symplectic form and Hamiltonian on the four‑dimensional parameter space of a kink‑antikink superposition ansatz, we construct an explicit perturbative Darboux transformation to all orders in the small parameter $\varepsilon = e^{-\mu s}$, where $s$ is the kink‑antikink separation and $\mu$ the decay rate of the static ...
Timmermans, Alexander, Kalmykov, Anton
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Chiralization of star-products and the isomorphisms of deformations and quantizations of Kleinian singularities

This thesis contains two directions of research, both related to the quantizations and deformations of Poisson structures. In the first part, we study the chiralization of star-products, a problem related to the quantization of Poisson vertex algebras.
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