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Poisson structures on certain moduli spaces for bundles on a surface

Johannes Huebschmann (1995)

Annales de l'institut Fourier

Let Σ be a closed surface, G a compact Lie group, with Lie algebra g , and ξ : P Σ a principal G -bundle. In earlier work we have shown that the moduli space N ( ξ ) of central Yang-Mills connections, with reference to appropriate additional data, is stratified by smooth symplectic manifolds and that the holonomy yields a homeomorphism from N ( ξ ) onto a certain representation space Rep ξ ( Γ , G ) , in fact a diffeomorphism, with reference to suitable smooth structures C ( N ( ξ ) ) and C Rep ξ ( Γ , G ) , where Γ denotes the universal central extension of...

Positive energy quantization of linear dynamics

Jan Dereziński, Christian Gérard (2010)

Banach Center Publications

The abstract mathematical structure behind the positive energy quantization of linear classical systems is described. It is separated into three stages: the description of a classical system, the algebraic quantization and the Hilbert space quantization. Four kinds of systems are distinguished: neutral bosonic, neutral bosonic, charged bosonic and charged fermionic. The formalism that is described follows closely the usual constructions employed in quantum physics to introduce noninteracting quantum...

Positive linear maps of matrix algebras

W. A. Majewski (2012)

Banach Center Publications

A characterization of the structure of positive maps is presented. This sheds some more light on the old open problem studied both in Quantum Information and Operator Algebras. Our arguments are based on the concept of exposed points, links between tensor products and mapping spaces and convex analysis.

Probability and quanta: why back to Nelson?

Piotr Garbaczewski (1998)

Banach Center Publications

We establish circumstances under which the dispersion of passive contaminants in a forced flow can be consistently interpreted as a Markovian diffusion process.

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